Landscape of solutions in constraint satisfaction problems
Marc Mezard, Matteo Palassini, Olivier Rivoire
TL;DR
This paper introduces a theoretical framework and practical algorithms to analyze the geometric structure of solutions in constraint satisfaction problems, exemplified by the coloring problem.
Contribution
It provides a novel framework for characterizing solution spaces and applies it to obtain detailed insights into the coloring problem's solution distribution.
Findings
Total number of solutions for the coloring problem calculated
Distribution of distances between solutions analyzed
Framework applicable to other CSPs
Abstract
We present a theoretical framework for characterizing the geometrical properties of the space of solutions in constraint satisfaction problems, together with practical algorithms for studying this structure on particular instances. We apply our method to the coloring problem, for which we obtain the total number of solutions and analyze in detail the distribution of distances between solutions.
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