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A Deterministic Distributed 2-Approximation for Weighted Vertex Cover in \(O(\log N\log \varDelta /\log ^2\log \varDelta )\) Rounds

  • Ran Ben-BasatEmail author
  • Guy Even
  • Ken-ichi Kawarabayashi
  • Gregory Schwartzman
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11085)

Abstract

We present a deterministic distributed 2-approximation algorithm for the Minimum Weight Vertex Cover problem in the CONGEST model whose round complexity is \(O(\log n\log \varDelta / \log ^2\log \varDelta )\). This improves over the currently best known deterministic 2-approximation implied by [KVY94]. Our solution generalizes the \((2+\epsilon )\)-approximation algorithm of [BCS17], improving the dependency on \(\epsilon ^{-1}\) from linear to logarithmic. In addition, for every \(\epsilon =(\log \varDelta )^{-c}\), where \(c\ge 1\) is a constant, our algorithm computes a \(\left( 2+\epsilon \right) \)-approximation in \(O(\log {\varDelta }/\log \log {\varDelta })\) rounds (which is asymptotically optimal).

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Ran Ben-Basat
    • 1
    Email author
  • Guy Even
    • 2
  • Ken-ichi Kawarabayashi
    • 3
  • Gregory Schwartzman
    • 3
  1. 1.Department of Computer ScienceTechnionHaifaIsrael
  2. 2.School of Electrical EngineeringTel Aviv UniversityTel AvivIsrael
  3. 3.NIITokyoJapan

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