Phase transition and finite‐size scaling for the integer partitioning problem

@article{Borgs2001PhaseTA,
  title={Phase transition and finite‐size scaling for the integer partitioning problem},
  author={Christian Borgs and Jennifer T. Chayes and Boris G. Pittel},
  journal={Random Structures \& Algorithms},
  year={2001},
  volume={19}
}
We consider the problem of partitioning n randomly chosen integers between 1 and 2m into two subsets such that the discrepancy, the absolute value of the difference of their sums, is minimized. A partition is called perfect if the optimum discrepancy is 0 when the sum of all n integers in the original set is even, or 1 when the sum is odd. Parameterizing the random problem in terms of κ=m/n, we prove that the problem has a phase transition at κ=1, in the sense that for κ<1, there are many… 
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