TY - GEN

T1 - When LP is the cure for your matching woes

T2 - 18th Annual European Symposium on Algorithms, ESA 2010

AU - Bansal, Nikhil

AU - Gupta, Anupam

AU - Li, Jian

AU - Mestre, Julián

AU - Nagarajan, Viswanath

AU - Rudra, Atri

PY - 2010

Y1 - 2010

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=78349256713&partnerID=8YFLogxK

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U2 - 10.1007/978-3-642-15781-3_19

DO - 10.1007/978-3-642-15781-3_19

M3 - Conference contribution

AN - SCOPUS:78349256713

SN - 3642157807

SN - 9783642157806

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 218

EP - 229

BT - Algorithms, ESA 2010 - 18th Annual European Symposium, Proceedings

Y2 - 6 September 2010 through 8 September 2010

ER -