From primal-dual to cost shares and back : a stronger LP relaxation for the Steiner forest problem

J. Könemann, S. Leonardi, G. Schäfer, S.H.M. Zwam, van

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

14 Citations (Scopus)

Abstract

We consider a game-theoretical variant of the Steiner forest problem, in which each of k users i strives to connect his terminal pair (s i , t i ) of vertices in an undirected, edge-weighted graph G. In [1] a natural primal-dual algorithm was shown which achieved a 2-approximate budget balanced cross-monotonic cost sharing method for this game. We derive a new linear programming relaxation from the techniques of [1] which allows for a simpler proof of the budget balancedness of the algorithm from [1]. Furthermore we show that this new relaxation is strictly stronger than the well-known undirected cut relaxation for the Steiner forest problem. We conclude the paper with a negative result, arguing that no cross-monotonic cost sharing method can achieve a budget balance factor of less than 2 for the Steiner tree and Steiner forest games. This shows that the results of [1,2] are essentially tight.
Original languageEnglish
Title of host publicationAutomata, Languages and Programming (Proceedings 32rd International Colloquium, ICALP 2005, Lisbon, Portugal, July 11-15, 2005)
EditorsL. Caires, G.F. Italiano, L. Monteiro, C. Palamidessi, M. Yung
Place of PublicationBerlin
PublisherSpringer
Pages930-942
ISBN (Print)3-540-27580-0
DOIs
Publication statusPublished - 2005

Publication series

NameLecture Notes in Computer Science
Volume3580
ISSN (Print)0302-9743

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