Approximating minimum-power degree and connectivity problems

Guy Kortsarz, Vahab S. Mirrokni, Zeev Nutov, Elena Tsanko

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


Power optimization is a central issue in wireless network design. Given a (possibly directed) graph with costs on the edges, the power of a node is the maximum cost of an edge leaving it, and the power of a graph is the sum of the powers of its nodes. Motivated by applications in wireless networks, we consider several fundamental undirected network design problems under the power minimization criteria. Given a graph with edge costs and degree requirements {r(v):v ∈ V}, the Minimum-Power Edge-Multi-Cover ( ) problem is to find a minimum-power subgraph of so that the degree of every node v is at least r(v). We give an O(logn)-approximation algorithms for , improving the previous ratio O(log4 n) of [11]. This is used to derive an O(logn + α)-approximation algorithm for the undirected Minimum-Power k -Connected Subgraph ( ) problem, where is the best known ratio for the min-cost variant of the problem (currently, = O(In k) for n ≥ 2k2 and otherwise). Surprisingly, it shows that the min-power and the min-cost versions of the k -Connected Subgraph problem are equivalent with respect to approximation, unless the min-cost variant admits an o(logn)-approximation, which seems to be out of reach at the moment. We also improve the best known approximation ratios for small requirements. Specifically, we give a 3/2-approximation algorithm for with r(v) ∈ {0,1}, improving over the 2-approximation by [11], and a -approximation for the minimum-power 2-Connected and 2-Edge-Connected Subgraph problems, improving the 4-approximation by [4]. Finally, we give a 4 r max -approximation algorithm for the undirected Minimum-Power Steiner Network ( ) problem: find a minimum-power subgraph that contains r(u,v) pairwise edge-disjoint paths for every pair u,v of nodes.

Original languageEnglish
Title of host publicationLATIN 2008
Subtitle of host publicationTheoretical Informatics - 8th Latin American Symposium, Proceedings
PublisherSpringer Verlag
Number of pages13
ISBN (Print)3540787720, 9783540787723
StatePublished - 2008
Event8th Latin American Theoretical INformatics Symposium, LATIN 2008 - Buzios, Brazil
Duration: 7 Apr 200811 Apr 2008

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume4957 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference8th Latin American Theoretical INformatics Symposium, LATIN 2008


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