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Improved Deterministic Distributed Matching via Rounding

Author Manuela Fischer

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LIPIcs.DISC.2017.17.pdf
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Keywords
  • distributed graph algorithms
  • deterministic distributed algorithms
  • rounding linear programs
  • maximal matching
  • maximum matching approximation

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Abstract

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 Delta log n)-round deterministic distributed algorithm for computing a maximal matching, in n-node graphs with maximum degree Delta. This is the first improvement in about 20 years over the celebrated O(log^4 n)-round algorithm of Hanckowiak, Karonski, and Panconesi [SODA'98, PODC'99].

- A deterministic distributed algorithm for computing a (2+epsilon)-approximation of maximum matching in O(log^2 Delta log(1/epsilon) + log^* n) rounds. This is exponentially faster than the classic O(Delta + log^* n)-round 2-approximation of Panconesi and Rizzi [DIST'01]. With some modifications, the algorithm can also find an epsilon-maximal matching which leaves only an epsilon-fraction of the edges on unmatched nodes.

- An O(log^2 Delta log(1/epsilon) + log^* n)-round deterministic distributed algorithm for computing a (2+epsilon)-approximation of a maximum weighted matching, and also for the more general problem of maximum weighted b-matching. These improve over the O(log^4 n log_(1+epsilon) W)-round (6+epsilon)-approximation algorithm of Panconesi and Sozio [DIST'10], where W denotes the maximum normalized weight.

- A deterministic local computation algorithm for a (2+epsilon)-approximation of maximum matching with 2^O(log^2 Delta) log^* n queries. This improves almost exponentially over the previous deterministic constant approximations which have query-complexity of 2^Omega(Delta log Delta) log^* n.

Cite As Get BibTex

Manuela Fischer. Improved Deterministic Distributed Matching via Rounding. In 31st International Symposium on Distributed Computing (DISC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 91, pp. 17:1-17:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017) https://doi.org/10.4230/LIPIcs.DISC.2017.17

Author Details

Manuela Fischer

References

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