On the computational complexity of the virtual network embedding problem
Given a graph representing a substrate (or physical) network with node and edge capacities and a set of virtual networks with node capacity demands and node-to-node traffic demands, the Virtual Network Embedding problem (VNE) calls for an embedding of (a subset of) the virtual networks onto the subs...
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| Vydané v: | Electronic notes in discrete mathematics Ročník 52; s. 213 - 220 |
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| Hlavní autori: | , , , |
| Médium: | Journal Article |
| Jazyk: | English |
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Elsevier B.V
01.06.2016
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| ISSN: | 1571-0653, 1571-0653 |
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| Abstract | Given a graph representing a substrate (or physical) network with node and edge capacities and a set of virtual networks with node capacity demands and node-to-node traffic demands, the Virtual Network Embedding problem (VNE) calls for an embedding of (a subset of) the virtual networks onto the substrate network which maximizes the total profit while respecting the physical node and edge capacities. In this work, we investigate the computational complexity of VNE. In particular, we present a polynomial-time reduction from the maximum stable set problem which implies strong NP-hardness for VNE even for very special subclasses of graphs and yields a strong inapproximability result for general graphs. We also consider the special cases obtained when fixing one of the dimensions of the problem to one. We show that VNE is still strongly NP-hard when a single virtual network request is present or when each virtual network request consists of a single virtual node and that it is weakly NP-hard for the case with a single physical node. |
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| AbstractList | Given a graph representing a substrate (or physical) network with node and edge capacities and a set of virtual networks with node capacity demands and node-to-node traffic demands, the Virtual Network Embedding problem (VNE) calls for an embedding of (a subset of) the virtual networks onto the substrate network which maximizes the total profit while respecting the physical node and edge capacities. In this work, we investigate the computational complexity of VNE. In particular, we present a polynomial-time reduction from the maximum stable set problem which implies strong NP-hardness for VNE even for very special subclasses of graphs and yields a strong inapproximability result for general graphs. We also consider the special cases obtained when fixing one of the dimensions of the problem to one. We show that VNE is still strongly NP-hard when a single virtual network request is present or when each virtual network request consists of a single virtual node and that it is weakly NP-hard for the case with a single physical node. |
| Author | Amaldi, Edoardo Coniglio, Stefano Tieves, Martin Koster, Arie M.C.A. |
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| Cites_doi | 10.1007/BF02392825 10.1016/j.comnet.2010.12.011 10.1145/1355734.1355737 10.1016/0304-3975(76)90059-1 10.1007/BF02943300 10.7155/jgaa.00183 10.1016/j.comnet.2009.10.017 |
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| References | Poljak (br0100) 1974; 15 Yu, Yi, Rexford, Chiang (br0110) 2008; 38 Geng, Zhang (br0070) 1986; 1 Andersen (br0010) 2002 Chowdhury, Boutaba (br0020) 2010; 54 Coniglio, Koster, Tieves (br0040) 2015 Eppstein (br0050) 2009; 13 Hastad (br0080) 1999; 182 Houidi, Louati, Ben-Ameur, Zeghlache (br0090) 2011; 55 Zhu, Ammar (br0120) 2006 Coniglio, Grimm, Koster, Tieves, Werner (br0030) 2015 Garey, Johnson, Stockmeyer (br0060) 1976; 1 Geng (10.1016/j.endm.2016.03.028_br0070) 1986; 1 Zhu (10.1016/j.endm.2016.03.028_br0120) 2006 Coniglio (10.1016/j.endm.2016.03.028_br0030) Hastad (10.1016/j.endm.2016.03.028_br0080) 1999; 182 Coniglio (10.1016/j.endm.2016.03.028_br0040) 2015 Yu (10.1016/j.endm.2016.03.028_br0110) 2008; 38 Andersen (10.1016/j.endm.2016.03.028_br0010) 2002 Houidi (10.1016/j.endm.2016.03.028_br0090) 2011; 55 Eppstein (10.1016/j.endm.2016.03.028_br0050) 2009; 13 Garey (10.1016/j.endm.2016.03.028_br0060) 1976; 1 Poljak (10.1016/j.endm.2016.03.028_br0100) 1974; 15 Chowdhury (10.1016/j.endm.2016.03.028_br0020) 2010; 54 |
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| SubjectTerms | combinatorial optimization computational complexity inapproximability Virtual network embedding |
| Title | On the computational complexity of the virtual network embedding problem |
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