Department of Computer Science | Institute of Theoretical Computer Science

Theory of Combinatorial Algorithms

Prof. Emo Welzl

We study the behavior of simple principal pivoting methods for the P-matrix linear complementarity problem (P-LCP). We solve an open problem of Morris by showing that Murty's least-index pivot rule (under any fixed index order) leads to a quadratic number of iterations on Morris's highly cyclic P-LCP examples. We then show that on K-matrix LCP instances, \emph{all} pivot rules require only a linear number of iterations. As the main tool, we employ \emph{unique-sink orientations} of cubes, a useful combinatorial abstraction of the P-LCP.