English

The Fr\'echet Contingency Array Problem is Max-Plus Linear

Optimization and Control 2009-04-16 v1

Abstract

In this paper we show that the so-called array Fr\'echet problem in Probability/Statistics is (max, +)-linear. The upper bound of Fr\'echet is obtained using simple arguments from residuation theory and lattice distributivity. The lower bound is obtained as a loop invariant of a greedy algorithm. The algorithm is based on the max-plus linearity of the Fr\'echet problem and the Monge property of bivariate distribution.

Keywords

Cite

@article{arxiv.0904.2244,
  title  = {The Fr\'echet Contingency Array Problem is Max-Plus Linear},
  author = {Laurent Truffet},
  journal= {arXiv preprint arXiv:0904.2244},
  year   = {2009}
}
R2 v1 2026-06-21T12:51:27.486Z