When LP is the cure for your matching woes: Improved bounds for stochastic matchings (extended abstract)

Nikhil Bansal, Anupam Gupta, Jian Li, Julián Mestre, Viswanath Nagarajan, Atri Rudra

Research output: Chapter in Book/Report/Conference proceedingConference contribution


Consider a random graph model where each possible edge e is present independently with some probability p e . We are given these numbers p e , and want to build a large/heavy matching in the randomly generated graph. However, the only way we can find out whether an edge is present or not is to query it, and if the edge is indeed present in the graph, we are forced to add it to our matching. Further, each vertex i is allowed to be queried at most t i times. How should we adaptively query the edges to maximize the expected weight of the matching? We consider several matching problems in this general framework (some of which arise in kidney exchanges and online dating, and others arise in modeling online advertisements); we give LP-rounding based constant-factor approximation algorithms for these problems. Our main results are: • We give a 5.75-approximation for weighted stochastic matching on general graphs, and a 5-approximation on bipartite graphs. This answers an open question from [Chen et al. ICALP 09]. • Combining our LP-rounding algorithm with the natural greedy algorithm, we give an improved 3.88-approximation for unweighted stochastic matching on general graphs and 3.51-approximation on bipartite graphs. • We introduce a generalization of the stochastic online matching problem [Feldman et al. FOCS 09] that also models preference-uncertainty and timeouts of buyers, and give a constant factor approximation algorithm.

Original languageEnglish (US)
Title of host publicationAlgorithms, ESA 2010 - 18th Annual European Symposium, Proceedings
Number of pages12
EditionPART 2
StatePublished - 2010
Event18th Annual European Symposium on Algorithms, ESA 2010 - Liverpool, United Kingdom
Duration: Sep 6 2010Sep 8 2010

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
NumberPART 2
Volume6347 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference18th Annual European Symposium on Algorithms, ESA 2010
Country/TerritoryUnited Kingdom

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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