Node Ranking Strategy in Virtual Network Embedding:An Overview

Shengchen Wu,Hao Yin,Haotong Cao,Longxiang Yang*,Hongbo Zhu*

1 College of Communication and Information Engineering,Nanjing University of Posts and Telecommunications,Jiangsu,Nanjing 210003,China

2 Institute of Electronic System Engineering,Beijing 10039,China

3 The Hong Kong Polytechnic University,26680 Kowloon,Hongkong,Hong Kong,China

Abstract:Network virtualization(NV)is a highprofile way to solve the ossification problem of the nowadays Internet,and be able to support the diversified network naturally.In NV,Virtual Network Embedding(VNE)problem has been widely considered as a crucial issue,which is aimed to embed Virtual Networks(VNs)onto the shared substrate networks(SNs)efficiently.Recently,some VNE approaches have developed Node Ranking strategies to drive and enhance the embedding efficiency.Node Ranking Strategy rank/sort the nodes according to the attributes of the node,including both residual local attributes(CPU,Bandwidth,storage,Etc.)and the global topology attributes(Number of neighborhood Nodes,Delay to other nodes,Etc.).This paper presents an overview of Node Ranking Strategies in Virtual Network Embedding,and possible directions of VNE Node Ranking Strategy.

Keywords:network virtualization;virtual network embedding;global topology attribute;node ranking

I.INTRODUCTION

In the past decades,the Internet has become one of the most important infrastructure for our society.The success of the Internet is dependent on various and different infrastructure technologies to support protocols and distributed applications[1].For the further consideration,the diversification of internet needs diverse network designs and paradigms,which could support old protocols and distributed applications,and open to innovation.However,the current internet architecture is barely impossible to adopt any new,innovative technologies,because it is required to get an agreement of many stakeholders of Internet Service Providers(ISPs).This is the network ossification problem[2].The ossification problem of the current Internet limited the development of network technologies and imposed the improvement of internet services.In this context,network virtualization(NV)has been highly concerned as a method to solve this ossification problem[3–7],and it has successfully been used in some testbeds and projects,including CABO[8],PlanetLab[9],G-Lab[10]and 4WARD[11].

Network virtualization proposed to decouple infrastructure providers(manage the physical infrastructures)from service providers(create virtual networks(VNs)from physical infrastructures to offer users services)in the traditional ISPs[3,12].As a result,a new internet business model needed and include two entities:infrastructure providers(InPs)and service providers(SPs).The SPs create Virtual Network Requests(VNRs)according to the user services,and send to InPs;InPs embed Virtual Networks(VNs)on substrate networks according to the VNRs sent by SPs.In this process,one of the key problem is how to allocate the requested virtual networks onto the substrate network effectively and efficiently;this is the so-called virtual network embedding(VNE)problem[13,14].(See Figure 1)

Figure 1.Virtual Network Embedding Scenario.

VNE problem is NP-hard[15],and it is really complicated and difficult to get the ideal/best solution.Even in off-line status or the locations where virtual nodes are pre-determined,it is simplified but still NPhard[16].In order to optimize the resource allocation,and get the optimal mapping solution,many VNE algorithms have been proposed[17–19].In recent years,many VNE algorithms use Node Ranking Strategy to drive and enhance the embedding efficiency.Node Ranking Strategy rank/sort the nodes according to the metrics of the node,including both residual local Resources metrics(CPU,Bandwidth,storage,etc.)and the global topology metrics(Number of neighborhood Nodes,Delay to other nodes,etc.).

Actually,Node Ranking Strategy is not a new notion,but it has just become a hot idea in recent years,and draws many attentions in academia.At the early stage,Node Ranking Strategy is not highlighted.It is used to select the assigned substrate nodes from a set of eligible substrate nodes,and only consider one or several residual local Resource attributes,like CPU capacity,or bandwidth.With the rank of nodes,it is easy to use“Greedy”algorithm to select the optimal substrate node.Compared with“greedy”node mapping algorithm,it is more expensive and complex to try other strategies,such as iterative methods[20,21]and simulated annealing[22].However,with the development of VNE algorithm,it is found that the global topology attributes remarkable impact on the efficiency and success-ratio of embedding result.Inspired by PageRank used by Google’s search engine,more and more authors use the same theory to rank/sort nodes with considering global resources and topology attributes[23–27].This strategy is used to rank the substrate nodes and virtual nodes of required virtual networks.Upon most occasions,the Virtual node with highest rank will be picked out first to embed,because the heavier the weight means more resources needed to be allocated.Same reason,in most instances,“Greedy”algorithm is employed to allocate the virtual node to substrate node;However there exists some exceptions,For example in[28],the author use node ranking approach to select the root node for TO-DPSO VNE algorithm,and employ DPSO algorithm to allocate the virtual node to substrate node.In some algorithms,all nodes of the substrate networks are ranked in order to pick the richest substrate node;However some researchers holds different ideas[23,24,29–33].In these algorithms,they first select the candidate nodes for each virtual node according to the location constrains or resource requirements.With continuous research,more and more VNE Algorithms with Node Ranking Strategy is proposed.

Node Ranking Strategy VNE brings many advantages.Each VN can be embedded in polynomial time;It can be promoted to discrete time event and continuous time event;With Enhanced and coordinated Node-Ranking algorithms,it can ensure better VN embedding to achieve the embedding goal.According to different requirements of VN services,different type of attributes could be defined and developed.As a result,Node Ranking Strategy becomes more and more popular,and it is treated as a most convent way to consider the network topology,global resources and VN service quality.

Previous papers have addressed many VNE algorithms with Node Ranking strategy.Based on previous works,this paper will present and analyze these works,and possible directions for the future research of VNE Node Ranking Strategy will be proposed by the end of this paper.The remainder of this paper is organized as follows:Section II describes the VNE Node Ranking Strategy,analyzes the Node Ranking procedure and Modelling.The typical VNE algorithm with Node Ranking Strategy are stated and summarized in Section III.Section IV highlights emerging research directions in the VNE Node Ranking Strategy and concludes this survey.

II.VNE NODE RANKING STRATEGY DESCRIPTION

In the previous literature,many different kinds of VNE algorithms with Node Ranking Strategy have been proposed to improve the embedding efficiency.In this section,a concise description and modelling of VNE Node Ranking Strategy is present here.VNE Node Ranking Strategy is a kind of approach to solving VNE problems.So before describing the Node Ranking Strategy,here Virtual Network Embedding problem and its objective is introduced first.

2.1 Virtual Network Embedding Problem

2.1.1 Substrate Network

The substrate network is the physical layer network,which is belonging to the InPs(Infrastructure Provider).The InPs design and operate the substrate network so that it can fulfill the virtual network request from SPs.The substrate network is constitutive of substrate nodes(routers,switches,etc.),substrate links(Cable,Fiber,etc.).

Usually a substrate network is expressed by a weighted graph.whichNSis the set of substrate nodes,andLSis the set of substrate links.is expressive of the attributes of substrate nodes,including available CPU,available Storage,node Location,etc.is expressive of the attributes of substrate links,including available Bandwidth,Delay,BRE(Bit-Error-Rate),etc.

In Figure 1,there is a simple VNE network scenario.The substrate network is constructed by six nodes and six links.The red number in Yellow Square-box is available CPU of this substrate node.The red number in Cream-colored Square-box is available bandwidth of this substrate link.Other attributes(like Node-Location,available Storage,Delay,BRE(Bit-Error-Rate),etc.)are not considered in this scenario.

2.1.2 Virtual Network

The virtual network is designed by the SPs according to the requirements of end-users.The SPs send the VN request to InPs to lease substrate resources.The virtual network is constitutive of virtual nodes and virtual links.Logically,Different virtual networks are independent from each other,even though they share the same substrate resources.

Generally,a virtual network is expressed by a weighted graph.whichNVis the set of virtual nodes,andLVis the set of virtual links.is expressive of the attributes of virtual nodes,including required CPU,required Storage,node Location,etc.is expressive of the attributes of virtual links,including required Bandwidth,constrained Delay,constrained BRE(Bit-Error-Rate),etc.

In Figure 1,there are two requested virtual networks,VN1 and VN2.The red number in Yellow Square-box is required CPU of this virtual node.The red number in Cream-colored Square-box is required bandwidth of this virtual link.Other attributes(like Node-Location constrains,required Storage,Delay constrains,BRE(Bit-Error-Rate)constrains etc.)are not considered in this scenario.

2.1.3 Virtual Network Embedding

The process to map the requested virtual network to the existing substrate network is called VNE.All the virtual nodes and links should be assigned to the substrate nodes and path(a path is a set of links which is connecting two nodes),at the same time all the requirements and constraints of virtual nodes and links should be satisfied,or we say embedding failed,request denied.The aim here is to allocate the substrate network resources in optimal way.

Generally,we express the VNE procedure as a function:.NEis a set of substrate nodes,which virtual nodes are mapped to,andPEis a set of substrate path,which the virtual links are mapped to.Substrate path is a set of substrate links,which connect two substrate nodes.is expressive of the attributes of substrate nodes,which is allocated to thisGV.is expressive of the attributes of substrate links,which is allocated to thisGV.Bothandshould fulfill the requirements and constrains ofGV.

In Figure 1,there are two virtual networks,which is embedded to the same substrate network.For VN1,andis embedded toand.For VN2,,andis embedded toand.All requirements and constrains of both VN1 and VN2 are fulfilled.

Normally,the whole VNE procedure also could be divided into two main stage,Node-Embedding and Link-Embedding.In Algorithm 1,we can see the Baseline Algorithm of VNE.In Node-Embedding stage,each node in virtual network will be assigned to one different substrate node.This procedure could be expressed as a function.In Link-Embedding stage,according to the topology of virtual network,each link will be mapped to one substrate path(unsplittable flow)or a set of substrate paths(splittable flow).Each substrate path connect the substrate nodes,which host the end virtual nodes.This procedure could be expressed as a function.

Also,except for the two stage VNE algorithm,there are also some one stage style algorithms,like RW-BFS Algorithm[23].However,no matter one stage or two stage,the aims is the same.

Algorithm 1.Baseline algorithm.1:While there are unprocessed VNRs 2:take one VNR:V NRi 3:do node embedding for V NRi 4:if node embedding for V NRi is failed then 5:Reject V NRi 6:Break 7:else 8:mapping the virtual nodes of V NRi to the substrate nodes 9:end if 10:do link embedding for V NRi 11:if link embedding for V NRi is failed then 12:Reject V NRi 13:Break 14:else 15:mapping the virtual links of V NRi to the substrate paths 16:end if 17:EndWhile

2.2 Objectives

The aims of VNE approach is to maximize the revenue of InP;minimize the cost of InP;provide stable VN service for SP and etc.As a result,when there are multiple solutions to embed the VN to the substrate network,and we need to find the optimal solution.There are some different objectives,which we need to work on.

Revenue-Cost-Ratiois defined as a Revenue divided by the Cost,and be expressed as functionR/C.Revenue is defined as the sum of the virtual network resources,which are embedded to the substrate network successfully.Generally,bandwidth and CPU is the main resources considered.Obviously,the Revenue could be expressed as function:Re（GV）[1].Cost is defined as the sum of the substrate network resources,which we allocated to the virtual network.Same as revenue,considering bandwidth and CPU,the cost could be expressed as function:Cost（F(GV →GS)）

It reflects the benefits for the cost of InPs.To maximize R/C is an important objective of VNE algorithm.In the other word,it is an important metric to evaluate a VNE algorithm.

Acceptance-Ratiois defined as the number of VNR which embedded successfully,divided by the number of total VNRs that arrive,and be expressed as functionIt reflects the service ability.With same substrate resources and virtual network requests,the higher Acceptance-Ratio means better service ability.

Disposition Time-periodis also called embedding time period of the virtual network requests.It is the time gap,between the time of virtual network request arrival and the time of virtual network deposited.It reflects the service speed.

2.3 Node Ranking Strategy Description and Modelling

As we defined in above,Node Ranking Strategy rank/-sort the nodes according to the attributes of the node,including both residual local attributes and the global topology attributes.There are three main steps for Node Ranking Strategy.The first step is to set the Node Ranking Attributes as shown in(4);the second step is to calculate the Node Ranking Value with Node Ranking Approach as shown in(5);the third step is to service the node mapping Algorithm with Node Ranking List as shown in(6).

2.3.1 Set Node-Ranking Attributes

Node-Ranking Attributes are the attributes of the object-network,which are used for Node Ranking.They are the parameters for Node Ranking Approach operation,and during operation,different authors would consider different Attributes.In the beginning,only the very basic attributes will be considered,like CPU Capacity,and Bandwidth Capacity.With the in-depth research,more and more Attributes are considered into Node-Ranking Attributes[34];and for same attributes,different author have different understanding.Obviously,it shows that reasonable consideration and analysis of Attributes could make the node evaluation more efficient and exact.In this literature,Node-Ranking Attributes are distributed into three categories,which are Network Resource Measurement(NRM),Network Topology Measurement(NTM),Service Optimize Measurement(SOM).

NRM Attributes are trying to measure the Network Resource,like CPU,Bandwidth etc.Different Attributes measure the Resource from different aspects,like counting the number of Virtual Network Objects,measure the amount of residual Resource,the Utilization Ratio or measure different resources and give a comprehensive score.As we mentioned before,VNE approach is aim to optimize the resource allocation,and get the optimal mapping solution.Therefore NRM Attribute is the fundamental type of attribute,which should be considered by all VNE approaches.Here we list some NRM attributes:

Node Stress:It is defined as the number of virtual nodes that are assigned to the substrate node[35].The Node Stress of nodenican be denoted as:S(ni).

CPU Capacity:It is defined as the remaining CPU resource of a substrate node,or the required CPU resource of a virtual node.The CPU Capacity of nodenican be denoted as:CPU(ni).

Table 1.Node-ranking attributes.

Link Stress:It is defined as the number of virtual links whose substrate path passes through the substrate link[35].The Link Stress of linklican be denoted as:S(li).

Bandwidth Capacity:It is defined as the residual bandwidth of a substrate link,or the required bandwidth of a virtual node.The Bandwidth Capacity of nodenican be denoted as:BW(li).

Node Strength:It is defined as the total outgoing residual bandwidth of a substrate node,or the total outgoing required bandwidth of a virtual node[36,37,33].The Strength of nodenican be denoted as:Strength(ni).

Node Capacity:It is defined as the residual resource amount of a substrate node,or the required resource amount of a virtual node.Usually,CPU Capacity of the node and Bandwidth Capacity of connected links are the two main resources,which are considered.The CPU Capacity of nodenican be denoted as:C(ni).As an example,in[16],author define Node Capacity as:

However some authors hold different understanding.In[38,39],the authors believe that the Bandwidth Capacity should be divided by two,since the bandwidth of each link is shared with its adjacent node.Then they redefine Node Capacity asC′(ni):

CPU Difference:The CPU Difference is define as the difference value of Substrate Node CPU Capacity minus Virtual Node CPU requirements[33].CPU utilization plays the main role in VNE energy consumption.

Flow Variable:A Flow Variable is defined as the total amount of flow on the substrate links for embedding a virtual link[40].Flow Variable is measuring the total amount of bandwidth occupied on the substrate for embedding a virtual link.

Correlation Quality:Correlation Quality reflect resource utilization of mapping.It considers the available bandwidth resources and hops of substrate paths,from the unmapped selected node to other assigned node[41].The substrate node with larger Correlation Quality supposed to hold a higher priority selected as the mapped node.

CPU Utilization Ratio:The CPU Utilization Ratio of the substrate node can be defined as the ratio between the required CPU capacity of a virtual node and the available CPU capacity of the substrate node[42].

Resource Consumption Ratio:Resource Consumption Ratio is define as the ratio of the CPU capacity and the storage capacity[43].It is to balance the CPU load and the storage load,in order to accept more VNRs.Especially in data center environments,the storage resource is one of the important constraint.

NTM Attributes are trying to show the role of a node in a network topology,to check whether the node is the centrality of a network or edge of it,how far the node from the others.Different Attributes measure the role of a node in the network from different aspects,like counting the Hops to others,measure the connectivity of a node.Actually,at the very beginning,NTM Attribute is not highlighted.With more and more literatures proves that it brings higher longterm average revenue and acceptance ratio to consider NTM Attributes.Therefore,in past few years,more and more author study on it.Here we list some kind of these attributes:

HOPS:HOPS is defined as the number of hops in a path between two nodes,can be denoted as:HOPni,nj[41,42].

Node Location:It is the location of a Node,expressed by a two dimension coordinates.The Location ofnican be denoted as:Loc(ni)or(xni,yni).

Node Distance:It is defined as the distance of two nodes,which is connected at least by one straight path in the network[44,25,45].Inspired by Euclidean distance,(xni,yni)and(xnj,ynj)are the coordinate location of nodeniandnj,then the Node Distance betweennjandnican be denoted as:Dis(ni,nj).

Node Closeness:Closeness centrality is one of the basic concepts in a topological space[46].Here in network,It shows how close this node to others in the network.Node Closeness is defined as the reciprocal of the sum of distances to all other nodes[47].The degree of nodenscan be denoted as:Closeness(ns).

D(ni,nj)is the number of edges in the geodesic linkingniandnj.

However,in[48],the author defined Node Closeness defined above as Classical Closeness Centrality and proposed a new Improved ClosenessCloseness′(ns)inspired by Gaussian Function.Apart from distance,author also take Bandwidth Capacity and CPU Capacity of path into consideration.The author believes that the improved closeness is adapting to the constantly changing networks.

Node Degree:It is defined as the number of links,connected to neighbourhood of a node[25,49,29].This metric reflect the connectivity and extensibility of a node,which is the ability of interactive with other nodes in the network.The degree of nodenscan be denoted as:Degree(ns).

Clustering Coefficient:The clustering coefficient reflect the connectivity of node.The clustering coefficient describes the ratio of neighbours to each other in the network[29].The clustering coefficient of nodenscan be denoted as:CC(ns).

Link Interference:The link interference attribute is trying to measure its contribution to the network connectivity.It originates form minimum interference-based traffic engineering,first studied in the MPLS context[37,50].

Location Importance:Location Importance reflect the location importance of one node.in the network.Stimulated from the known Coulomb’s law in electromagnetism area,we can quantify the location interaction between any two different nodes.[45].

Node Betweenness:Betweenness centrality is a notion of traffic volume that goes from a node to another node and must pass through this assumed node[51].The traffic volume of a node can be measure by how many shortest path between go through this node.[52].

SOM Attributes are trying to reflect some indicators at the service level.With considering SOM Attributes,the approaches is not only trying to consider the problem of embedding VNs,but also consider how to guarantee the quality of the VN service and decrease the cost of the service.Here we list some kind of these attributes:

Node Reliability:The Node Reliability reflect the reliability of node according to its reliability and its connected link reliability[53].The Node Reliability of nodenscan be denoted as:r(ns).Since the really Reliability of a node is not only effect by the node itself,but also its neighbour nodes;the author in[53]come up with a attribute called CMNR,which is Comprehensive Metric of Node Reliability,and can be denoted as:CMNR(ns).

Link Delay:The Link Delay is represented by the path length,since the transmission delay of a physical link isDelay(ni,nj)=Length(ni,nj)/c,cis the speed of signal[26].cis the speed of signal in transmission,if in fiberc=2×105km/s[54].Usuallycis much larger than the Length of a substrate link.In order to make the calculation simple,in some articles[37,55],author set link delay of Each substrate as one time unit.

Node Energy Cost:Node Energy Cost defined as the additional power consumption for assign a virtual node to a substrate node[24].

2.3.2 Calculate the Node Ranking Value with Node Ranking Approach

Node Ranking Approach is the operation of evaluating each node according the Node-Ranking Attributes.The evaluation result of node is usually called Node Ranking Value.As we mentioned above,different author use different attributes as the input,however even with same input,the Node Ranking Value also could be different because of the different Approaches.The better Node Ranking Approach could make the Node Ranking Value more accurate,so that the Node Ranking Strategy could be more valuable and efficient.Here we list three type of approaches:

Basic Approach:Considering the Node Ranking Attributes above,Basic Approach get the Node Ranking Value by Simple Mathematical Calculation,which are referring to Addition Subtraction Multiplication and Division.Just like,In[16]the author defined the amount of residual Resources as the Node Ranking Value,which CPU Capacity and Bandwidth Capacity are considered,and denoted asH′(ns)Basic Approach is the simplest compared with the other types of Approaches,and quite efficient.However,since algorithms which based on Basic Approach only consider the local Resource attributes,the longterm performance(the long-term average revenue,the long-term R/C ratio and the long-term acceptance ratio)is not as good as the algorithms which based on other types of Approaches(PageRank Theory Approach and MADM Approach),like:RW-MaxMatch Algorithm,TOP-MANR Algorithm.

PageRank Theory Approach:PageRank Theory Approach considers topology-aware resource of a node,which reflects the resource and quality of connections of a node.PageRank Theory originally is used by Google’s search engine,which measures the popularity of web pages.PageRank considers a link from page A to page B as a vote,and a page is considered important,if a number of important pages vote to it.In VNE,PageRank considers a link from node A to node B as a vote,a node is considered important,if a number of important nodes vote to it.

As a example,In[23],the author use PageRank Theory Approach defineNR(u)as the Node Ranking Value of Nodenu.CPU Capacity and Bandwidth Capacity are the attributes considered,Same as Equation(12).In Equation(13),The Normalization is employed since with normalization the accuracy of the model could be Improved,and the convergence rate of the model is increased.According to PageRank Theory,the Node Ranking value is shown as Equation(16).The Node Ranking Value could be calculated by using Iterations scheme;and T is a one-step transition matrix of the Markov chain.

Inspired by Google PageRank,PageRank Theory Approach offers a good solution to consider the resource and quality of a node and its connections at the same time.When embedding a VN,not only the resources availability or requirements are taken into account,but also the resource quality which the substrate node is connected.As a result,it improves the performance of long-term average revenue,R/C ratio and the VNR acceptance ratio is outstanding.

MADM Approach:MADM is short for Multiple Attribute Decision Making.MADM Approach is based on MADM method.MADM is applied in the evaluation facet,which is usually associated with a limited number of predetermined alternatives and discrete preference ratings.Since we should consider lots of different attributes in the node mapping process,MADM method is one mature and effective solution for considering multi-attributes together.In[41,56,42],Some MADM methods(TOPSIS[57]and ELECTRE[58,59])have already been proved that it works excellent.First,the metric values of every attributes should be calculated for each node,the decision making matrix can be formulated as follow:

Each element in the matrixaijrepresents the metric value of attribute-j for nodeni.Similar with above approach,we can Normalize,weight and modify the decision making matrix.Finally,calculate the relative Value(ELECTRE-Net domain Value;TOPSISCloseness based on Euclidean Distances)of the matrix as the node ranking value.

MADM Approach offers a better solution for considering different kind of attributes together,compared with the other types of Approaches above.In other types of Approaches,for each node finally we get a comprehensive Node Ranking Value.In MADM Approaches,all kinds of attributes are listed in the decision making matrix separately;and they are weighted and modified separately.In[41,42,56],under same condition,this type of Approaches outperforms the above two type VNE algorithms in terms of the long-term average revenue,the long-term R/C ratio and the VNR acceptance ratio.

2.3.3 Service the NoM Algorithm with Node Ranking List

Node Ranking List is a list of nodes Ranked according to the Node Ranking Value.In the VNE Node Ranking Strategy,it’s usually employed by the Node Mapping Algorithm(NoM-Algorithm).Here some of the NoMAlgorithms with Node Ranking List are introduced.

Basic Greedy algorithm:It sorts virtual nodes in non-increasing order according to their Node Rank values.Virtual Nodes with higher rank get embedding service first.During embedding,it always pick the Substrate Node with highest rank in the list,which meets all the requirements of Virtual Node at the same time.“Greedy”node mapping algorithm is the most popular one,since it is computationally too expensive to employ other strategies.Basic greedy algorithm is to map the virtual nodes to the substrate nodes with the maximum substrate resources so that it can minimize the use of the resources at the bottleneck nodes.It is beneficial to future requests,which may require specific substrate nodes with scarce resources,so that It could improve the Acceptance Ratio,and C/R Ratio.

L2S2 algorithm:Based on basic Greedy algorithm,L2S2 algorithm also sorts virtual nodes in nonincreasing order according to their Node Rank values,and does the same on substrate nodes.With the two Node Ranking Lists,mapsto,provided that the CPU capacity and the link capacity ofcan meet what nodeasks for.For convenience,the author call this mapping algorithm L2S2[23,60](which stands for“large-to-large and small-to-small”).L2S2 algorithm is similar to Basic Greedy algorithm,and faster.The virtual nodes are mapped to the substrate nodes according to their ranking in each list.However it cannot guarantee the corresponding ranking substrate node always meets what the virtual node required,so that it leads a lower acceptance ratio than the Basic Greedy algorithm.

2-Round Greedy algorithm:Based on basic Greedy algorithm,2-Round Greedy algorithm is using the greedy algorithm twice in one time,just like LTPIN Algorithm[31].In LTPIN,Firstly LNTPR(Locality-aware node topological potential ranking)Algorithm is used to rank all the nodes,and get the top n(n<6)nodes;Then LICN(Locality-aware influence choosing node)Algorithm is used to rank the selected n nodes to get the assigned node.In LNTPR Algorithm,nodes are evaluated by the topological potential,which is similar with the improved closeness.In LICN,nodes are evaluated by node influence(18).LTPIN Algorithm is also based on the Greedy algorithm,but it gives us an idea to rank nodes in two stages with different facets,not one standard.The specific flow of LTPIN is shown in Figure 2.The 2-Round Greedy algorithm LTPIN leads a higher acceptance ratio and R/c ratio than the one which uses LNTPR only.

Figure 2.LTPIN Algorithm Flow-Chart.

niis one of the substrate candidate nodes for the virtual node.

npis the substrate node which is allocated to the parent node of the virtual node.(Parent node is the connected node at upper level in the BFS tree.)

Pshortest(ni,np)is the shortest path betweenniandnp.

Probability and Random algorithm:Probability and Random algorithm is going to calculate a Probability for each candidate substrate node,according to their Rank based on basic Greedy algorithm[61,40].Higher rank,larger Probability.Then Randomly assign the virtual node to substrate nodes,based on their Probability.There is one precondition,which is all candidate substrate nodes reach all requirements of the virtual node.In the same condition,the Probability and Random algorithm is not as good as Greedy algorithms in terms of the average provisioning cost.However,in networks with large numbers of nodes,Probability and Random algorithm has been proved that it works better for load balancing[40],and leads higher acceptance ratio than greedy algorithm.

III.ANALYSIS OF TYPICAL NODE RANKING STRATEGIES

In this section,we are going to categorize the different VNE Node Ranking Strategies.Classification tables are given here.Some Typical Node Ranking Strategies will be introduced in details,and be analysed.

3.1 A Taxonomy of Node Ranking Strategies

3.1.1 Node-Ranking Attributes Range

Attributes Range refers to the range of Attributes,when Calculating the NR-Value.As showed in(5),when we Calculate theNRV alue(ni),we uses the.In this paper,we classify Attributes Range into three categories,which are Local,Neighbour and Global,and we can separateinto three parts,ni,N′,N′′.Then we can expressNRV alue(ni)as(19).

Local Range:For Local Range,the author only consider the attributes of the local node which isni.These Node Ranking Strategies are classified as Local Range Node Ranking Strategies.In(19),andare ZERO;the NR-Value isIn[16]This is a typical Local Range Node Ranking Strategies.The considered attributes are the available bandwidth and CPU resources of the node.

Neighbour Range:For Neighbour Range,the attributes of the local node and its neighbour nodes are considered.These Node Ranking Strategies are classified as Neighbour Range Node Ranking Strategies.In(19),is ZERO;the NR-Value is.

Global Range:For Global Range,the attributes of all nodes are considered.These Node Ranking Strategies are classified as Global Range Node Ranking Strategies.In(19),none ofis ZERO;the NR-Value is.

3.1.2 Node-Ranking Nodes Scale

Node-Ranking Nodes Scale refers to the Scale of node,which are going to be ranked.As showed in(5),it is the size ofN.Usually,there are two type,Full Nodes and Selected Nodes.Here we only discuss about the situation,when we rank the substrate nodes;because if it is to rank the virtual nodes,absolutely all virtual nodes will be ranked.

Full Nodes:All nodes in the network are candidate nodes,so all nodes are ranked.It is quite simple and effective.Usually the nodes which own larger resources,will be on the top of the list.It is easy to find the suitable node from all nodes.Usually,one counter will be set.If unfortunately the first top node is not qualified,will decrease the counter and try the second top node.If failed again,it goes the same way until counter ends.

Selected Nodes:Select candidate nodes from the network,then pick the assigned one according to their rank.It takes more steps,but will reduce the Scale of candidate nodes.Usually,there are two different ways to select the candidates node.The first is to select the qualified substrate nodes,which meets all requirements of the virtual node;and the second is to select candidate nodes,according to some of constrains.

3.2 The Introduction of Typical Node Ranking Strategies

3.2.1 Local Range VNE Algorithm

In Local Range VNE Algorithms,Some works select candidate substrate nodes,which satisfy restrictions,and rank these selected nodes.Some of them are introduced as follow:

Table 2.LR(local range)category.

2008 M.Yu proposed a Base-Line VNE Algorithm[16].As a Base-line algorithm,others usually pick it up as a reference.Only available local CPU capacity and node capacity is considered.The virtual nodes are ranked according to the Node Capacity.Candidate substrate nodes are the substrate nodes,which fulfill the requirements of the assigned virtual node.The candidate substrate nodes are ranked according to the CPU capacity.Virtual nodes are picked according to their rank,and mapped to the substrate nodes with basic greedy algorithm.It makes efficient use of the underlying resources.

2009 N.M.M.K.Chowdhury proposed two Algorithms,D-ViNE and R-ViNE[61].Only available amount of flow for each node is considered.In the two algorithms,a corresponding meta-node is created for each virtual node.Each corresponding meta-node is connected with all the candidate substrate nodes by infinite bandwidth meta-edges.Candidate substrate nodes are the substrate nodes,which fulfill the requirements of the assigned virtual node.The candidate substrate nodes are ranked according to their available amount of flow.In D-ViNE,Virtual nodes are mapped to the substrate nodes with basic greedy algorithm.In R-ViNE,Virtual nodes are mapped to the substrate nodes with Probability and Random algorithm.Both the proposed algorithms increase the acceptance ratio and the revenue while decreasing the cost incurred by the substrate network in the long run.For networks with large numbers of nodes,R-ViNE has been shown to be more effective for load balancing than D-ViNE.In 2012,based on D-ViNE and RViNE,N.M.M.K.Chowdhury proposed ViNEYard algorithms,which are a collection of VN embedding algorithms that leverage better coordination between the two phases[40].

In Local Range VNE Algorithms,Some other works rank the full nodes of the network.Some of them are introduced as follow:

2013 M.Feng proposed a topology-aware VNE algorithm based on the degrees of nodes[49],which advocate utilizing topological attributes of substrate and virtual networks in the VNE problem.Based on typical Node Capacity and node degree,the node ranking value is calculated with Basic Approach.All nodes(both virtual nodes and substrate nodes)are ranked according to their node ranking value.Virtual nodes are picked according to their rank,and mapped to the substrate nodes with basic greedy algorithm.Topologyaware VNE algorithm has achieved higher long-term average revenue,acceptance ratio,and RC ratio at the same time than all the 4 previous algorithms,Base-line algorithm[16].Random Walk algorithm[23],classical closeness centrality algorithm[48],hybrid algorithm[62].

2018 P.Zhang proposed two Algorithms,NRMVNE and RCR-VNE Algorithms[43].Storage resource constraints on substrate nodes and virtual nodes are considered and discussed.Based on typical Node Capacity and node Storage,Basic Approach is employed to calculate the node ranking value,and Basic greedy algorithm is used to perform the node mapping.In NRM-VNE,All nodes(both virtual nodes and substrate nodes)are ranked according to their node ranking value.In RCR-VNE,different node ranking value is adopted to virtual node and substrate nodes.Substrate nodes are ranked according to their resource consumption ratio.The NRM-VNE algorithm is slightly better than the RCR-VNE algorithm in terms of Long-Term Average Revenue and Long-Term Revenue to Cost(R/C)Ratio.

3.2.2 Neighbour Range VNE Algorithm

In Neighbor Range VNE Algorithms,there are few works selecting candidate substrate nodes,which satisfy restrictions,and ranking these selected nodes.Some of them are introduced as follow:

2016 S.Gong proposed an Algorithm,TOP-MANR[41].Based on CPU Capacity,Bandwidth Capacity,node degree,node closeness,node distance and Hops,the node ranking value is calculated with MADM Approach,TOPSIS method.Candidate substrate nodes are the substrate nodes,which meet the requirements of the assigned virtual node.Both virtual nodes and candidate substrate nodes are ranked according to the node ranking value.Virtual nodes are mapped to the candidate substrate nodes with basic greedy algorithm.TOP-MANR outperforms Base-line algorithm[16],RW-MaxMatch Algorithm[23]and IC-VNE[48]in terms of the long-term average revenue,the long-term R/C ratio and the VNR acceptance ratio under different conditions of VNRs.In addition,L.Shooshtarian holds the similar idea,and in 2019 he proposed an Algorithm NSGAII-VDCE[56]based on TOP-MANR.He is trying to explore the application of Node Ranking Strategy VNE algorithm in VDC(Virtual data center)embedding issue with considering robustness for data center infrastructure and avoiding imbalance mapping.

2017 P.Zhang proposed an Algorithm VNE-DCC[29].The node degree and the clustering coefficient information is considered and discussed.Based on typical Node Capacity,node degree and the clustering coefficient information,Basic Approach is employed to calculate the node ranking value.In the node mapping stage,the Breadth First Search is employed,so that a BFS tree is built.Virtual node which has the largest node ranking value is the root,and mapped to the substrate node which owns the greatest node ranking value.For each other virtual nodes,candidate substrate nodes are the neighbor nodes of the node,which the virtual node’s parent node assigned.Then Basic greedy algorithm is adopted for the node mapping.Compared with Base-line algorithm[16],RW-MaxMatch Algorithm[23],VNE-DCC algorithm improves the performance of VN embedding procedure in terms of R/C ratio and acceptance ratio,as well as decreases the scaling factor.Based on VNE-DCC,2018 P.Zhang proposed another Algorithm RDCC-VNE[53],with considering node reliability.In RDCC-VNE,author incorporate the reliability probability of substrate nodes into the VNE process to improve the QoS/QoE of end users from a new perspective.

In Neighbor Range VNE Algorithms,some works rank the full nodes of the network.Several of them are introduced as follow:

2014 L.Gong proposed an Algorithm GRC-VNE[63].Based on CPU Capacity and Bandwidth Capacity,the node ranking value is calculated with PageRank Theory Approach.In[63],the node ranking valueis called global resource capacity(GRC)metric,which is indicate that Neighbor nodes’ resource are considered to evaluate the node.Here in this paper,we call this Neighbor Range,since some other works consider the real full global nodes’ resource when evaluation.All nodes(both virtual nodes and substrate nodes)are ranked in a descending order according to the node ranking value,respectively;Then Basic Greedy algorithm is used for node mapping.It shows that GRCVNE algorithm generates a higher revenue and a lower blocking probability than the two previous algorithms,RW-MaxMatch Algorithm[23]and Topology-aware VNE algorithm[49].

Table 3.NR(neighbour range)category.

2016 F.Bianchi proposed an Algorithm MCRR[39],based on Markov Reward Processes,which associates a metric which accounts for and well captures the amount of local resources available in a vicinity of a given node.Based on typical Node Capacity,the node ranking value is calculated with PageRank Theory Approach.All nodes(both virtual nodes and substrate nodes)are ranked according to their node ranking value;Then Basic Greedy algorithm is used for node mapping.Compared with GRC-VNE Algorithm[63],RW-MaxMatch Algorithm[23],and Topologyaware VNE algorithm[49],MCRR improves the VNE performance in terms of lower blocking probability and higher revenues and balanced resources utilization.

2018 P.Zhang proposed an Algorithm Simplified ELECTRE-VNE[42].Based on HOPS,Node Degree,Node Capacity,Bandwidth Capacity and CPU Utilization Ratio,the node ranking value is calculated with MADM Approach,simplified ELECTRE method.The virtual nodes are ranked according to the Node Capacity.The substrate nodes are ranked according to node ranking value.Then Basic greedy algorithm is adopted for the node mapping.Simulation in the paper shows that Simplified ELECTRE-VNE outperforms the Base-line algorithm[16],RW-MaxMatch Algorithm[23]and IC-VNE[48]in terms of the long-term average revenue,the long-term R/C ratio,and the VN request acceptance ratio.

3.2.3 Global Range VNE Algorithms

In Global Range VNE Algorithms,there are a few works selecting candidate substrate nodes,which satisfy restrictions,and ranking these selected nodes.Some of them are introduced as follow:

2011 X.Cheng proposed an Algorithm,RW-BFS[23],which also employ BFS tree as[29].Based on Typical Node Capacity,the node ranking value is calculated with by PageRank Theory Approach,and also adopted to rank both virtual and substrate nodes.Then Basic Greedy algorithm is used for node mapping on the basis of BFS.It show that our algorithms outperform the previous approach Base-line algorithm[16],in terms of the long-term average revenue and the VNR acceptance ratio.

2014 S.Su proposed an Algorithm,EA-VNE[24].In EA-VNE,Candidate substrate node list is constructed first.Then Based on energy cost and Typical Node Capacity,the node ranking value is calculated with PageRank Theory Approach,and is used for ranking candidate substrate nodes.Then Basic Greedy algorithm is used for node mapping.An energy cost model is proposed,and the experimental results show that EA-VNE can save up to 50%energy cost for ISPs than the Optimal algorithm(ViNEYard algorithm)in[40].Based on EA-VNE,2018 H.Cao proposed another Algorithm,ER-VNE[33].In ER-VNE,more topology attributes is considered,like Node Degree,Node Closeness,Link Interference.PageRank Theory Approach and Basic Greedy algorithm is adopted.ERVNE saves approximately 16% energy cost than EAVNE,and achieve equal acceptance ratio at the same time.

2014 D.Zhang proposed an Algorithm,LTPIN[31].Based on Node Distance,CPU Capacity,the node ranking value is calculated with by Basic Approach,and is adopted for ranking both virtual and substrate nodes.BFS method also adopted in LTPIN,and the virtual node with highest node ranking value is the root node.Root node is also assigned to the substrate node with highest node ranking value.For other virtual node,it select top n(n<6)of substrate node ranking which can satisfy the requirement of the virtual node as substrate candidate nodes.Then based on Node Influence,a new node ranking value is calculated with Basic Approach.According to the 2-Round Greedy algorithm,the virtual node is mapped to the node with highest new node ranking value.Compare with RW-MM[23],It decrease the cost,since in the second round node ranking,Node Influence considered the path between candidate nodes and substrate nodes of its parents node.

2018 Y.Zong proposed an Algorithm,GTR-VNE[26].Based on CPU Capacity,Bandwidth Capacity and Node Distance,the node ranking value is calculated with PageRank Theory Approach.All nodes(both virtual nodes and substrate nodes)are ranked in a descending order according to the node ranking value.Candidate node is established if the substrate nodes satisfy the requirements of the virtual node.Then Basic Greedy algorithm is used for node mapping.Compared with Base-line algorithm[16],GTR-VNE outperforms the benchmarks in terms of power consumption,R/C ratio and acceptance ratio.What’s more,based on GTR-VNE,Y.Zong also proposed ACOVNE Algorithm with considering power consumption.Compared with GTR-VNE,the total power consumption has been reduced by around 20%.

2018 M.Lu proposed an Algorithm,RIM-ViNE[30]based on R-ViNE[61].Same as R-ViNE,Probability and Random algorithm is adopted for node map-ping.However with PageRank Theory Approach,the node Value are measured by not only Node Capacity but also multiple topological attributes,such as Node Degree,Classic Node Closeness.In RIM-ViNE,Link Value measurement is also introduced.Both node and link Value are used to set the embedding cost of thesubstrate network resources,effectively avoiding excessive use of critical nodes and links from the previous VNRs with small resource VN requirements.

Table 4.GR(global range)category–Part I:Selected node group.

Table 5.GR(global range)category–Part II:Full node group.

In Global Range VNE Algorithms,some works rank the full nodes of the network.Several of them are introduced as follow:

2011 X.Cheng proposed an Algorithm,RW-MM[23].Based on Typical Node Capacity,the node ranking value is calculated with PageRank Theory Approach,and is used for ranking both virtual and substrate nodes.Then Basic Greedy algorithm is used for node mapping.It achieved a higher acceptance ratio,higher revenue than Base-line algorithm[16].Based on RW-MM,2018 P.Zhang proposed another Algorithm RRW-MM[53],with considering node reliability.In RRW-MM,author incorporate the reliability probability of substrate nodes into the VNE process to improve the QoS/QoE of end users from a new perspective.

2012 Z.Wang proposed an Algorithm,lmproved Closeness VNE[48].Based on lmproved Closeness,the node ranking value is calculated with Basic Approach,and is adopted for ranking both virtual and substrate nodes.Then Basic Greedy algorithm is used for node mapping.Compared with CIassical CIoseness VNE,Improved Closeness VNE increase the acceptance ratio and the revenue while decreasing the cost incurred by the substrate network.

2017,H.Cao proposed an Algorithms,VNETAGRD[25].Node Distance,Node Degree,Node Strength,CPU Capacity are considered.PageRank Theory Approach is adopted for calculating Node Ranking Value,which is used to ranking both virtual and substrate nodes.Then mapping node with Basic Greedy algorithm.On the basis of three fundamental topology attributes and global network resources,VNE-TAGRD rank all substrate and virtual nodes before conducting each VNR embedding.Compared with RW-MM[23],Base-line algorithm[16],VNEDCC[29]and NRM-VNE[43],VNE-TAGRD have a better performance in terms of the long-term average VNR acceptance ratio and average revenue to cost ratio.

2018,H.Cao proposed an Algorithms,VNENTANRC[37]which considering Node Distance,Node Degree,Node Strength,Link Interference,Node Farness and Closeness and CPU Capacity.The Node ranking approach and Node Mapping algorithm is the same with his work in 2017 VNE-TAGRD,however More topology attributes considered.Compared with Base-line algorithm[16],RW-MM[23],VNERD[66],VNE-DCC[29]and NRM-VNE[43],VNENTANRC have a better performance in terms of the long-term average VNR acceptance ratio,average revenue to cost ratio,and Average Node and Link Utilization.

2020,H.Cao proposed an Algorithms,VNE-ARS[27]which considering Node Degree,Node Strength,Node Closeness,Node Centrality,CPU Capacity and Bandwidth Capacity.Using PageRank Theory Approach,the SN and VN nodes values are calculated.Then mapping node with Basic Greedy algorithm.In addition,there is a virtual link embedding checking,after each node embedded.If there exists unmapped virtual link between mapped virtual nodes,the link is going to be mapped immediately.Compared with VNE-RD[66],VNE-DCC[29],VNE-TAGRD[25]and VNE-RIM[30],VNE-ARS outperformance in terms of VNR Acceptance Ratio,VNE revenue to cost ratio and Utilization of CPU and Bandwidth.

3.3 A Summary for the Existing Researches

As what we introduced above,more than half of the works are proposed in recent 5 years.Now the node ranking Strategy VNE algorithms have been well researched.

Different Node Value Approaches are employed to evaluate the node value.With development of researches,less and less researchers use Basic Node Ranking Approach.With MADM Approaches,VNE algorithms usually consider more attributes than the other two types of approaches,since it offers a better solution for considering different kind of attributes together.With PageRank Theory Approach,VNE algorithms usually consider larger range of resources,since it offers a good solution to consider global resources.In these node ranking approaches,they also ought to try more Node Ranking method,especially the MADM Approach.In existing MADM Approach works[41,42,56],only TOPSIS(Technique for Order Preference by Similarity to Ideal Solution)and ELECTRE(ELimination Et Choice Translating REality)are studied and discussed.However,there exist many other MADM Approach Methods[67],like:SAW(Simple Additive Weighting),PROMETHEE(Preference Ranking Organization Methods for Enrichment Evaluations)and VIKOR(VlseKriterijumska Optimizacija I Kompromisno Resenje).With these new methods,more extra node ranking algorithms could be proposed.

Multiple“Greedy”based NoM algorithms are proposed.Even through the Basic Greedy algorithm is widely used,we want to introduce the other“Greedy”based NoM algorithms emphatically,such as L2S2 algorithm,2-Round Greedy algorithm and Probability and Random algorithm.L2S2 is more fast;2-Round Greedy algorithm gives an idea to rank nodes in two stages with different facets;Probability and Random algorithm provide a random embedding solution based on Greedy algorithm.These algorithms could be considered,improved or deeply studied in the future researches.

More works choose to rank selected substrate candidate nodes.These algorithms need to be highlighted,because they always selected these nodes for some purposes.Such as:decreasing the scaling factor[29];supporting meta-node mapping idea[61,30];using BFS scheme[23,31,29,64];Or decreasing the computational complexity[24,32,33].These purposes are also worthy to be considered in the future works.

A variety of attributes are defined.However,there still exists a demand of researching and proposing more extra node ranking algorithms.While in current node ranking algorithms,considered and quantified NTM attributes are usually node degree,node closeness and distances,link strength,and link interference.However,there exist multiple other NTM attributes[34,68].Similar to the situation of NTM attributes,among SOM attributes,what usually be considered are Link Delay,Node Energy Cost and Node Reliability.There also exist other SOM attributes,like Node Security and Link Reliability.Therefore,there exist potential space for the research direction of proposing more node ranking algorithms.In these node ranking algorithms,they ought to consider and quantify more Network Topology Measurement(NTM)and Service Optimize Measurement(SOM)attributes.By considering more and more attributes,the node ranking VNE algorithms can be equipped with stronger embedding abilities.In addition,while keep trying exploring new attributes,the researchers also can further study and discuss the existing attributes,especially comparing related attributes.In[43],author study and discuss the Resource Consumption Ratio and Node Capacity.There still are other related attributes.For example:node degree,Link Interference and node closeness are all network connectivity related;CPU Capacity,CPU Difference and CPU Utilization Ratio are all CPU resource related.Researchers can study on how these attributes effect on the VN embedding quality and what is their difference.For instance,the VNE algorithm 1 only considers the node degree while VNE algorithm 2 and 3 only considers the Link Interference and node closeness attribute accordingly.Researchers can compare these algorithms’ abilities of embedding virtual networks while giving the same physical network environment and VN request.This type of node ranking research can further optimize the choosing of attributes,while evaluating the nodes.

As we can see,Node Ranking Strategy VNE is still a research field with potential.

IV.CONCLUSION AND FUTURE DIRECTIONS

In this paper,we make a survey on the existing Node Ranking VNE solutions and categorize these solutions according to different aspects.For future work of Node Ranking VNE solution,this section highlights the future research directions and two main fields are mainly identified:

4.1 Integrate Wireless Resources to Assist Node Ranking

In current research of node ranking algorithms,the resources requiring to be allocated are usually CPU,node storage,node capacity and link bandwidth resources.These resources are generally considered as the resources in core network.Few VNE publications[69]considering wireless resources while doing the VNs embedding.Thus,to expand the allocated resource types,it is necessary to integrate the wireless resources.

As usual,wireless resources for being allocated are radio spectrum resource and wireless network infrastructures(base stations,random access points).

We can take one VN embedding in integrated wired and wireless networks as the example.The VN,requiring to be implemented and embedded,has the function of transmitting data to core data center.Thus,the topology of the VN can be a line,including two end nodes.One virtual node can be embedded onto the physical data center node while the other end node is a mobile device,such as a mobile phone.Since the mobile phone needs to be connect onto a nearest base station.The base station must reserve available radio spectrum resources for the phone to transmit data within its coverage cell.Since multiple phones coexist within the base station,the base station must allocate to its assigned radio resources in an effective and efficient manner so as to guarantee the transmitting quality of the phone.Meanwhile,the data flow must go through a secure and reliable between the data center and the base station.Therefore,it is necessary for the network provider to construct and reserve the secure and reliable physical path.The path has the function of transmitting data flow.If the known backhaul[70]is considered,the problem will be more complicated.

4.2 New Emerging Technologies and Applications Aspects

Recently,new emerging technologies arise.We select and discuss two hot emerging technologies that can be used to deal with node ranking VNE.

The first emerging technology to be discussed is the blockchain[71–73].Since current node ranking class of VNE algorithms focus on maximizing the number of accepted VNs and maximizing the total revenues of network service providers.No node ranking algorithm discussed the security purpose in the literature.

Since blockchain enables to ensure the data security,the blockchain framework and approach can be used in the node ranking VNE algorithm.As we known,the network element,no matter node or link,cannot be fully virtualized by the service provider.In real networking environment,the network element can be easily attacked by the malicious attackers or hacker.If attacked,the hacker may seize the control of the network element.Thus,its information running through the element can be easily detected and modified by the attacker.This will lead to the VN performance degradation eventually.

To deal with these security problem,the blockchainenabled framework and algorithms can be adopted.Till now,no relevant research on the blockchain framework is studied to deal with the VNE problem.The most related publication is[69],which used the RSA approach to define secure physical nodes to embed virtual nodes.Strictly speaking,[69]simply used one aspect of blockchain to deal with VNE.Thus,the node ranking VNE integrating blockchain technology can be further researched.

The other emerging technology that can be used to deal with node ranking VNE is the artificial intelligence(AI)and deep learning(DL)[74,75].By many rounds and iterations of trainings,the stronger nodes and links can be selected to conduct the VNE.Till now,few publications considering to add more topology attributes and DL approach exist.Some publications[76–78]simply consider one isolated topology attribute to rank nodes.

As a conclusion,Network Virtualization is a promising technology of overcoming the ossification of current network.VNE is the key technology in network Virtualization and allocates the substrate resource effectively and efficiently to the proposed virtual networks.Node Ranking strategy is one highlighted method which employed by VNE solutions.The VNE with Node Ranking Strategy is still an open field and covers many points.

ACKNOWLEDGEMENT

The authors would like to thank the reviewers for their detailed reviews and constructive comments,which have helped improve the quality of this paper.This work was supported by National Science Foundation of China under Grants 61871446.