2026-08-07T04:46:34Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:18843 2024-03-06T11:02:42Z ddc:004 open_access

An Approximation Algorithm for the Exact Matching Problem in Bipartite Graphs Dürr, Anita El Maalouly, Nicolas Wulf, Lasse Perfect Matching Exact Matching Red-Blue Matching Approximation Algorithms Bounded Color Matching In 1982 Papadimitriou and Yannakakis introduced the Exact Matching problem, in which given a red and blue edge-colored graph G and an integer k one has to decide whether there exists a perfect matching in G with exactly k red edges. Even though a randomized polynomial-time algorithm for this problem was quickly found a few years later, it is still unknown today whether a deterministic polynomial-time algorithm exists. This makes the Exact Matching problem an important candidate to test the RP=P hypothesis. In this paper we focus on approximating Exact Matching. While there exists a simple algorithm that computes in deterministic polynomial-time an almost perfect matching with exactly k red edges, not a lot of work focuses on computing perfect matchings with almost k red edges. In fact such an algorithm for bipartite graphs running in deterministic polynomial-time was published only recently (STACS'23). It outputs a perfect matching with k' red edges with the guarantee that 0.5k ≤ k' ≤ 1.5k. In the present paper we aim at approximating the number of red edges without exceeding the limit of k red edges. We construct a deterministic polynomial-time algorithm, which on bipartite graphs computes a perfect matching with k' red edges such that k/3 ≤ k' ≤ k. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Anita Dürr and Nicolas El Maalouly and Lasse Wulf 2023 Is Part Of LIPIcs, Volume 275, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.APPROX/RANDOM.2023.18 urn:nbn:de:0030-drops-188436 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2023.18 eng https://creativecommons.org/licenses/by/4.0/legalcode