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The linear programming relaxation permutation symmetry group of an orthogonal array defining integer linear program

2016; London Mathematical Society; Volume: 19; Issue: 1 Linguagem: Inglês

10.1112/s1461157016000085

1461-1570

David M. Arquette, Dursun A. Bulutoglu,

Optimization and Packing Problems

There is always a natural embedding of $S_{s}\wr S_{k}$ into the linear programming (LP) relaxation permutation symmetry group of an orthogonal array integer linear programming (ILP) formulation with equality constraints. The point of this paper is to prove that in the $2$ -level, strength- $1$ case the LP relaxation permutation symmetry group of this formulation is isomorphic to $S_{2}\wr S_{k}$ for all $k$ , and in the $2$ -level, strength- $2$ case it is isomorphic to $S_{2}^{k}\rtimes S_{k+1}$ for $k\geqslant 4$ . The strength- $2$ result reveals previously unknown permutation symmetries that cannot be captured by the natural embedding of $S_{2}\wr S_{k}$ . We also conjecture a complete characterization of the LP relaxation permutation symmetry group of the ILP formulation. Supplementary materials are available with this article.