J un 2 00 1 Statistical Mechanics of an NP-complete Problem : Subset Sum

  title={J un 2 00 1 Statistical Mechanics of an NP-complete Problem : Subset Sum},
  author={Tomohiro Sasamoto and Taro Toyoizumi and Hidetoshi Nishimori},
We study statistical properties of an NP-complete problem, the subset sum, using the methods and concepts of statistical mechanics. The problem is a generalization of the number partitioning problem, which is also an NP-complete problem and has been studied in the physics literature. The asymptotic expressions for the number of solutions are obtained. These results applied to the number partitioning problem as a special case are compared with those which were previously obtained by a different… CONTINUE READING

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