Enumeration of PLCP-orientations of the 4-cube
Abstract
The linear complementarity problem (LCP) provides a unified approach to many problems such as linear programs, convex quadratic programs, and bimatrix games. The general LCP is known to be NP-hard, but there are some promising results that suggest the possibility that the LCP with a P-matrix (PLCP) may be polynomial-time solvable. However, no polynomial-time algorithm for the PLCP has been found yet and the computational complexity of the PLCP remains open. Simple principal pivoting (SPP) algorithms, also known as Bard-type algorithms, are candidates for polynomial-time algorithms for the PLCP. In 1978, Stickney and Watson interpreted SPP algorithms as a family of algorithms that seek the sink of unique-sink orientations of -cubes. They performed the enumeration of the arising orientations of the -cube, hereafter called PLCP-orientations. In this paper, we present the enumeration of PLCP-orientations of the -cube.The enumeration is done via construction of oriented matroids generalizing P-matrices and realizability classification of oriented matroids.Some insights obtained in the computational experiments are presented as well.
Keywords
Cite
@article{arxiv.1309.7225,
title = {Enumeration of PLCP-orientations of the 4-cube},
author = {Lorenz Klaus and Hiroyuki Miyata},
journal= {arXiv preprint arXiv:1309.7225},
year = {2014}
}