Mittagsseminar (in cooperation with J. Lengler, A. Steger, and D. Steurer)

Date and Time: Tuesday, March 27, 2007, 12:15 pm

Duration: This information is not available in the database

Location: OAT S15/S16/S17

Speaker: Leo Rüst

The Hidden-K-Matrix Linear Complementarity Problem

Given a square matrix M and a vector q, the Linear Complementarity Problem (LCP) is to find nonnegative vectors w and z such that w-Mz=q and in every component either w or z is zero. The LCP has a unique solution for every q if and only if M is a P-matrix, a matrix whose principal minors are all positive. Hardness of the P-matrix LCP would imply that NP is equal to coNP, which is very unlikely. On the other hand, there is no polynomial time algorithm known.

In this talk we restrict our focus to the class of hidden-K-matrices, an interesting and nontrivial subclass of P-matrices known to be solvable in polynomial time. Up to now, hidden-K-matrices have been looked at only from an algebraic point of view. We shed some light onto the combinatorial structure of the hidden-K-matrix LCP, in particular we show that the orientation implicitly underlying a hidden-K-matrix LCP is acyclic for every q.

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