The demand query model for bipartite matching

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Abstract

We introduce a “concrete complexity” model for studying algorithms for matching in bipartite graphs. The model is based on the “demand query” model used for combinatorial auctions. Most (but not all) known algorithms for bipartite matching seem to be translatable into this model including exact, approximate, sequential, parallel, and online ones. A perfect matching in a bipartite graph can be found in this model with O(n3/2) demand queries (in a bipartite graph with n vertices on each side) and our main open problem is to either improve the upper bound or prove a lower bound. An improved upper bound could yield “normal” algorithms whose running time is better than the fastest ones known, while a lower bound would rule out a faster algorithm for bipartite matching from within a large class of algorithms. Our main result is a lower bound for finding an approximately maximum size matching in parallel: A deterministic algorithm that runs in no(1) rounds, where each round can make at most n1.99 demand queries cannot find a matching whose size is within no(1) factor of the maximum. This is in contrast to randomized algorithms that can find a matching whose size is 99% of the maximum in O(log n) rounds, each making n demand queries.

Original languageAmerican English
Title of host publicationACM-SIAM Symposium on Discrete Algorithms, SODA 2021
EditorsDaniel Marx
Pages592-599
Number of pages8
ISBN (Electronic)9781611976465
StatePublished - 2021
Event32nd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2021 - Alexandria, Virtual, United States
Duration: 10 Jan 202113 Jan 2021

Publication series

NameProceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

Conference

Conference32nd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2021
Country/TerritoryUnited States
CityAlexandria, Virtual
Period10/01/2113/01/21

All Science Journal Classification (ASJC) codes

  • Software
  • General Mathematics

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