The Even Outdegree Conjecture for Acyclic PLCP-Cubes in Dimension Five

Sonoko MORIYAMA  Yoshio OKAMOTO  

Publication
IEICE TRANSACTIONS on Information and Systems   Vol.E89-D   No.8   pp.2402-2404
Publication Date: 2006/08/01
Online ISSN: 1745-1361
DOI: 10.1093/ietisy/e89-d.8.2402
Print ISSN: 0916-8532
Type of Manuscript: INVITED PAPER (Special Section on Invited Papers from New Horizons in Computing)
Category: 
Keyword: 
linear complementarity problems,  unique sink orientations,  Holt-Klee condition,  

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Summary: 
The behavior of Bard-type pivoting algorithms for the linear complementarity problem with a P-matrix is represented by an orientation of a hypercube. We call it a PLCP-cube. In 1978, Stickney and Watson conjectured that such an orientation has no facet on which all even outdegree vertices appear. We prove that this conjecture is true for acyclic PLCP-cubes in dimension five.