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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Bibliographic Details
Published in:Electronic notes in discrete mathematics Vol. 52; pp. 213 - 220
Main Authors: Amaldi, Edoardo, Coniglio, Stefano, Koster, Arie M.C.A., Tieves, Martin
Format: Journal Article
Language:English
Published: Elsevier B.V 01.06.2016
Subjects:
combinatorial optimization
computational complexity
inapproximability
Virtual network embedding
combinatorial optimization
inapproximability
Virtual network embedding
computational complexity
ISSN:1571-0653, 1571-0653
Online Access:Get full text
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Summary: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.
ISSN:1571-0653
1571-0653
DOI:10.1016/j.endm.2016.03.028