research-article

Distributed half-integral matching and beyond

Authors:

Jukka SuomelaAuthors Info & Claims

Volume 982, Issue C

https://doi.org/10.1016/j.tcs.2023.114278

Published: 27 February 2024 Publication History

Abstract

By prior work, it is known that any distributed graph algorithm that finds a maximal matching requires Ω ( log ⁎ ⁡ n ) communication rounds, while it is possible to find a maximal fractional matching in O ( 1 ) rounds in bounded-degree graphs. However, all prior O ( 1 )-round algorithms for maximal fractional matching use arbitrarily fine-grained fractional values. In particular, none of them is able to find a half-integral solution, using only values from { 0, 1 2, 1 }. We show that the use of fine-grained fractional values is necessary, and moreover we give a complete characterization on exactly how small values are needed: if we consider maximal fractional matching in graphs of maximum degree Δ = 2 d, and any distributed graph algorithm with round complexity T ( Δ ) that only depends on Δ and is independent of n, we show that the algorithm has to use fractional values with a denominator at least 2 d. We give a new algorithm that shows that this is also sufficient.

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Index Terms

Distributed half-integral matching and beyond
1. Mathematics of computing
  1. Discrete mathematics
    1. Graph theory
2. Theory of computation
  1. Design and analysis of algorithms
    1. Distributed algorithms

Index terms have been assigned to the content through auto-classification.

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cover image Theoretical Computer Science

Theoretical Computer Science Volume 982, Issue C

Jan 2024

363 pages

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Elsevier Science Publishers Ltd.

United Kingdom

Publication History

Published: 27 February 2024

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