Hardness of robust network design

Authors:
C. Chekuri;F. B. Shepherd;G. Oriolo;M. G. Scutellá
Affiliations:
Lucent Bell Labs, 600 Mountain Ave, Murray Hill, New Jersey 07974;Lucent Bell Labs, 600 Mountain Ave, Murray Hill, New Jersey 07974;Dipartimento di Ingegneria dell'Impresa, via del Politecnico 1, 00133, Rome, Italy;Dipartimento di Informatica, Largo Bruno Pontecorvo 3, 56127, Pisa, Italy
Venue:
Networks
Year:
2007

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Abstract

The authors settle the complexity status of the robust network design problem in undirected graphs. The fact that the flow-cut gap in general graphs can be large, poses some difficulty in establishing a hardness result. Instead, the authors introduce a single-source version of the problem where the flow-cut gap is known to be one. They then show that this restricted problem is coNP-Hard. This version also captures, as special cases, the fractional relaxations of several problems including the spanning tree problem, the Steiner tree problem, and the shortest path problem. © 2007 Wiley Periodicals, Inc. NETWORKS, Vol. 50(1), 50–54 2007 A preliminary version has appeared in Proc INOC, (2005), 455–461.