Improved deterministic distributed matching via rounding

• Published in: Distributed computing Vol. 33; no. 3-4; pp. 279 - 291
• Main Author: Fischer, Manuela
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.06.2020; Springer Nature B.V
• Subjects: Algorithms; Approximation; Computation; Computer Communication Networks; Computer Hardware; Computer Science; Computer Systems Organization and Communication Networks; Graph matching; Mathematical analysis; Rounding; Software Engineering/Programming and Operating Systems; Theory of Computation; Weight
• ISSN: 0178-2770; 1432-0452
• DOI: 10.1007/s00446-018-0344-4

We present improved deterministic distributed algorithms for a number of well-studied matching problems, which are simpler, faster, more accurate, and/or more general than their known counterparts. The common denominator of these results is a deterministic distributed rounding method for certain linear programs , which is the first such rounding method, to our knowledge. A sampling of our end results is as follows: An O log 2 Δ · log n -round deterministic distributed algorithm for computing a maximal matching, in n -node graphs with maximum degree Δ . This is the first improvement in about 20 years over the celebrated O ( log 4 n ) -round algorithm of Hańćkowiak, Karoński, and Panconesi [SODA’98, PODC’99]. A deterministic distributed algorithm for computing a ( 2 + ε ) -approximation of maximum matching in O log 2 Δ · log 1 ε + log ∗ n rounds. This is exponentially faster than the classic O ( Δ + log ∗ n ) -round 2-approximation of Panconesi and Rizzi [DIST’01]. With some modifications, the algorithm can also find an almost maximal matching which leaves only an ε -fraction of the edges on unmatched nodes. An O log 2 Δ · log 1 ε · log 1 + ε W + log ∗ n -round deterministic distributed algorithm for computing a ( 2 + ε ) -approximation of a maximum weighted matching, and also for the more general problem of maximum weighted b -matching. Here, W denotes the maximum normalized weight. These improve over the O log 4 n · log 1 + ε W -round ( 6 + ε ) -approximation algorithm of Panconesi and Sozio [DIST’10].