Derandomization of the Mulmuley–Vazirani–Vazirani algorithm for Exact Matching

Determine whether the randomized polynomial-time algorithm of Mulmuley, Vazirani, and Vazirani (1987) for the Exact Matching problem can be derandomized to obtain a deterministic polynomial-time algorithm that, given a 0/1-weighted graph G and an integer k, decides whether G has a perfect matching of weight exactly k.

Background

The Exact Matching (EM) problem asks whether a given 0/1-weighted graph admits a perfect matching of a specified weight. Mulmuley, Vazirani, and Vazirani (1987) gave a randomized polynomial-time algorithm for EM via algebraic methods, which remains the primary general solution with polynomial running time.

The paper highlights that despite progress on special classes of graphs and various parameterized and relaxed variants, the question of whether the MVV randomized algorithm can be derandomized is explicitly still open.