License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2023.18
URN: urn:nbn:de:0030-drops-188436
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2023/18843/
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Dürr, Anita ; El Maalouly, Nicolas ; Wulf, Lasse

An Approximation Algorithm for the Exact Matching Problem in Bipartite Graphs

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LIPIcs-APPROX18.pdf (0.9 MB)

Abstract

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.

BibTeX - Entry

@InProceedings{durr_et_al:LIPIcs.APPROX/RANDOM.2023.18,
  author =	{D\"{u}rr, Anita and El Maalouly, Nicolas and Wulf, Lasse},
  title =	{{An Approximation Algorithm for the Exact Matching Problem in Bipartite Graphs}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023)},
  pages =	{18:1--18:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-296-9},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{275},
  editor =	{Megow, Nicole and Smith, Adam},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2023/18843},
  URN =		{urn:nbn:de:0030-drops-188436},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2023.18},
  annote =	{Keywords: Perfect Matching, Exact Matching, Red-Blue Matching, Approximation Algorithms, Bounded Color Matching}
}

Keywords: Perfect Matching, Exact Matching, Red-Blue Matching, Approximation Algorithms, Bounded Color Matching
Collection: Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023)
Issue Date: 2023
Date of publication: 04.09.2023

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