Work

Distributed Approximate Maximum Matching and Minimum Vertex Cover via Generalized Graph Decomposition

Year: 2026

Type: conference-paper

Abstract: The classic lower bound of Kuhn, Moscibroda and Wattenhofer [JACM 2016] states that approximate maximum matching and approximate vertex cover (among other problems) in the LOCAL model require Ω(min{log⁡nlog⁡log⁡n,log⁡Δlog⁡log⁡Δ}) rounds, for any polylogarithmic or smaller approximation ratio. As a function of Δ, this complexity was subsequently matched for constant-approximate weighted vertex cover [Bar-Yehuda, Censor-Hillel and Schwartzman, JACM 2017] and constant-approximate maximum matching [Bar-Yehuda, Censor-Hillel, Ghaffari and Schwartzman, PODC 2017]. One might expect, therefore, that the true complexity should be Θ(log⁡Δlog⁡log⁡Δ), and the n-dependent term in the lower bound is just an artefact of the proof method.

Source: ACM Symposium on Principles of Distributed Computing (PODC)

DOI: 10.1145/3796701.3815909

Author: Peter Davies-Peck

Institution: Durham University

Language: English

Topic: Complexity and Algorithms in Graphs

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Funder: Engineering and Physical Sciences Research Council

Award: Distributed Lovász Local Lemma