A Theory of Alternating Paths and Blossoms, from the Perspective of Minimum Length

Vijay V. Vazirani , University of California, Irvine.

It is well known that the proof of some prominent results in mathematics took a very long time — decades and even centuries. The first proof of the Micali-Vazirani (MV) algorithm, for finding a maximum cardinality matching in general graphs, was recently completed — over four decades after the publication of the algorithm (1980). MV is still the most efficient known algorithm for the problem. In contrast, spectacular progress in the field of combinatorial optimization has led to improved running times for most other fundamental problems in the last three decades, including bipartite matching and max-flow.

The new ideas contained in the MV algorithm, and its proof remain largely unknown, and hence unexplored. We hope to rectify this shortcoming and use ideas from the proof to give a simpler exposition of the algorithm.

Based on this paper.

Bio: Vijay Vazirani is a distinguished professor at the University of California, Irvine. A description of his research appears in the citation of his 2022 INFORMS John von Neumann Theory Prize. In 2001, he published Approximation Algorithms, which was followed by two co-edited books, Algorithmic Game Theory in 2007 and Online and Matching-Based Market Design in 2023.