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Positive linear programming, parallel approximation and PCP's

  • Luca Trevisan
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1136)

Abstract

Several sequential approximation algorithms are based on the following paradigm: solve a linear or semidefinite programming relaxation, then use randomized rounding to convert fractional solutions of the relaxation into integer solutions for the original combinatorial problem. We demonstrate that such a paradigm can also yield parallel approximation algorithms by showing how to convert certain linear programming relaxations into essentially equivalent positive linear programming [18] relaxations that can be near-optimally solved in NC. Building on this technique, and finding some new linear programming relaxations,we develop improved parallel approximation algorithms for Max Sat, Max Directed Cut, and MaxkCSP. We also show a connection between probabilistic proof checking and a restricted version of MaxkCSP. This implies that our approximation algorithm for MaxkCSP can be used to prove inclusion in P for certain PCP classes.

Keywords

Feasible Solution Approximate Algorithm Semidefinite Programming Linear Programming Relaxation Probabilistic Proof Check 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Luca Trevisan
    • 1
  1. 1.Dipartimento di Scienze dell'InformazioneUniversità di Roma La SapienzaRomaItaly

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