Gap Amplification in PCPs Using Lazy Random Walks

  • Jaikumar Radhakrishnan
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4051)


We show an alternative implementation of the gap amplification step in Dinur’s [4] recent proof of the PCP theorem. We construct a product G t of a constraint graph G, so that if every assignment in G leaves an ε-fraction of the edges unsatisfied, then in G t every assignment leaves an Ω()-fraction of the edges unsatisfied, that is, it amplifies the gap by a factor Ω(t). The corresponding result in [4] showed that one could amplify the gap by a factor \(\Omega(\sqrt{t})\). More than this small quantitative improvement, the main contribution of this work is in the analysis. Our construction uses random walks on expander graphs with exponentially distributed length. By this we ensure that some random variables arising in the proof are automatically independent, and avoid some technical difficulties.


Random Walk Original Graph Constraint Graph Product Construction Expander Graph 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Jaikumar Radhakrishnan
    • 1
    • 2
  1. 1.School of Technology and Computer ScienceTata Institute of Fundamental ResearchMumbaiIndia
  2. 2.Toyota Technological Institute at ChicagoChicagoUSA

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