Unsatisfiability Bounds for Random CSPs from an Energetic Interpolation Method

  • Dimitris Achlioptas
  • Ricardo Menchaca-Mendez
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7391)


The interpolation method, originally developed in statistical physics, transforms distributions of random CSPs to distributions of much simpler problems while bounding the change in a number of associated statistical quantities along the transformation path. After a number of further mathematical developments, it is now known that, in principle, the method can yield rigorous unsatisfiability bounds if one “plugs in an appropriate functional distribution”. A drawback of the method is that identifying appropriate distributions and plugging them in leads to major analytical challenges as the distributions required are, in fact, infinite dimensional objects. We develop a variant of the interpolation method for random CSPs on arbitrary sparse degree distributions which trades accuracy for tractability. In particular, our bounds only require the solution of a 1-dimensional optimization problem (which typically turns out to be very easy) and as such can be used to compute explicit rigorous unsatisfiability bounds.


Energy Function Interpolation Method Univariate Factor Degree Sequence Optimal Assignment 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Dimitris Achlioptas
    • 1
    • 2
    • 3
  • Ricardo Menchaca-Mendez
    • 3
  1. 1.University of AthensGreece
  2. 2.CTIGreece
  3. 3.University of CaliforniaSanta CruzUSA

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