## Abstract

In this paper we analyze the expected time complexity of the auction algorithm for the matching problem on random bipartite graphs. We first prove that if for every non-maximum matching on graph G there exist an augmenting path with a length of at most 2l + 1 then the auction algorithm converges after N {dot operator} l iterations at most. Then, we prove that the expected time complexity of the auction algorithm for bipartite matching on random graphs with edge probability w.h.p. This time complexity is equal to other augmenting path algorithms such as the HK algorithm. Furthermore, we show that the algorithm can be implemented on parallel machines with O(log(N)) processors and shared memory with an expected time complexity of O(Nlog(N)).

Original language | American English |
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Pages (from-to) | 384-395 |

Number of pages | 12 |

Journal | Random Structures and Algorithms |

Volume | 48 |

Issue number | 2 |

DOIs | |

State | Published - 1 Mar 2016 |

Externally published | Yes |

### Bibliographical note

Publisher Copyright:© 2014 Wiley Periodicals, Inc.

## Keywords

- Auction algorithm
- Bipartite matching
- Complexity
- Pushrelabel algorithm
- Random graphs