Universal Factor Graphs

  • Uriel Feige
  • Shlomo Jozeph
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7391)

Abstract

The factor graph of an instance of a symmetric constraint satisfaction problem on n Boolean variables and m constraints (CSPs such as k-SAT, k-AND, k-LIN) is a bipartite graph describing which variables appear in which constraints. The factor graph describes the instance up to the polarity of the variables, and hence there are up to 2 km instances of the CSP that share the same factor graph. It is well known that factor graphs with certain structural properties make the underlying CSP easier to either solve exactly (e.g., for tree structures) or approximately (e.g., for planar structures). We are interested in the following question: is there a factor graph for which if one can solve every instance of the CSP with this particular factor graph, then one can solve every instance of the CSP regardless of the factor graph (and similarly, for approximation)? We call such a factor graph universal. As one needs different factor graphs for different values of n and m, this gives rise to the notion of a family of universal factor graphs.

We initiate a systematic study of universal factor graphs, and present some results for max-kSAT. Our work has connections with the notion of preprocessing as previously studied for closest codeword and closest lattice-vector problems, with proofs for the PCP theorem, and with tests for the long code. Many questions remain open.

Keywords

Approximation Ratio Constraint Satisfaction Problem Factor Graph 3CNF Formula Sorting Network 
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 2012

Authors and Affiliations

  • Uriel Feige
    • 1
  • Shlomo Jozeph
    • 1
  1. 1.Department of Computer Science and Applied MathematicsThe Weizmann Institute of ScienceRehovotIsrael

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