The Stackelberg minimum spanning tree game

Jean Cardinal, Erik D. Demaine, Samuel Fiorini, Gwenaël Joret, Stefan Langerman, Ilan Newman, Oren Weimann

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

Abstract

We consider a one-round two-player network pricing game, the Stackelberg Minimum Spanning Tree game or STACKMST. The game is played on a graph (representing a network), whose edges are colored either red or blue, and where the red edges have a given fixed cost (representing the competitor's prices). The first player chooses an assignment of prices to the blue edges, and the second player then buys the cheapest possible minimum spanning tree, using any combination of red and blue edges. The goal of the first player is to maximize the total price of purchased blue edges. This game is the minimum spanning tree analog of the well-studied Stackelberg shortest-path game. We analyze the complexity and approximability of the first player's best strategy in STACKMST. In particular, we prove that the problem is APX-hard even if there are only two different red costs, and give an approximation algorithm whose approximation ratio is at most min{k, 3 + 2 In 6,1 + In W}, where k is the number of distinct red costs, b is the number of blue edges, and W is the maximum ratio between red costs. We also give a natural integer linear programming formulation of the problem, and show that the integrality gap of the fractional relaxation asymptotically matches the approximation guarantee of our algorithm.

Original languageEnglish
Title of host publicationAlgorithms and Data Structures - 10th International Workshop, WADS 2007, Proceedings
PublisherSpringer Verlag
Pages64-76
Number of pages13
ISBN (Print)3540739483, 9783540739487
DOIs
StatePublished - 2007
Event10th International Workshop on Algorithms and Data Structures, WADS 2007 - Halifax, Canada
Duration: 15 Aug 200717 Aug 2007

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume4619 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference10th International Workshop on Algorithms and Data Structures, WADS 2007
Country/TerritoryCanada
CityHalifax
Period15/08/0717/08/07

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science (all)

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