Approximating Maximum Matching Requires Almost Quadratic Time
Pages 444 - 454
Abstract
We study algorithms for estimating the size of maximum matching. This problem has been subject to extensive research. For n-vertex graphs, Bhattacharya, Kiss, and Saranurak [FOCS’23] (BKS) showed that an estimate that is within є n of the optimal solution can be achieved in n2−Ωє(1) time, where n is the number of vertices. While this is subquadratic in n for any fixed є > 0, it gets closer and closer to the trivial Θ(n2) time algorithm that reads the entire input as є is made smaller and smaller. In this work, we close this gap and show that the algorithm of BKS is close to optimal. In particular, we prove that for any fixed δ > 0, there is another fixed є = є(δ) > 0 such that estimating the size of maximum matching within an additive error of є n requires Ω(n2−δ) time in the adjacency list model.
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Index Terms
- Approximating Maximum Matching Requires Almost Quadratic Time
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June 2024
2049 pages
ISBN:9798400703836
DOI:10.1145/3618260
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- Igor Shinkar,
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Published: 11 June 2024
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