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The Cartographer
Exact Matching and the Top-k Perfect Matching Problem
September 17, 2022 Β· Declared Dead Β· π arXiv.org
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Authors
Nicolas El Maalouly, Lasse Wulf
arXiv ID
2209.09661
Category
cs.DS: Data Structures & Algorithms
Citations
4
Venue
arXiv.org
Last Checked
4 months ago
Abstract
The aim of this note is to provide a reduction of the Exact Matching problem to the Top-$k$ Perfect Matching Problem. Together with earlier work by El Maalouly, this shows that the two problems are polynomial-time equivalent. The Exact Matching Problem is a well-known 40 years old problem for which a randomized, but no deterministic poly-time algorithm has been discovered. The Top-$k$ Perfect Matching Problem is the problem of finding a perfect matching which maximizes the total weight of the $k$ heaviest edges contained in it.
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