Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

Date and Time: Tuesday, March 31, 2015, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: May Szedlák

Combinatorial Redundancy Detection Algorithm

The problem of detecting (and removing) redundant constraints is fundamental in optimization. We focus on the case where we are given a set H of n halfspaces in the d-dimensional real space. The feasible solution set is given by the intersection of all halfspaces in H and a halfspace is called redundant if its removal does not change the feasible solution set. The currently fastest known algorithm to detect all redundancies is the one by Clarkson. This method solves n linear programs, each of them on at most s variables, where s is the number of nonredundant variables. In this talk we study the combinatorial aspect of redundancy detection. How and how fast can we detect all redundant halfspaces? Instead of the linear system we only consider the finitely many signed dictionaries, i.e., matrices that can be thought of as an enriched version of an intersection point of d halfspaces of H. We show that given only this combinatorial information, there is an output sensitive algorithm to detect all redundancies. Although our running time is worse than Clarkson's, in the case where all constraints are in general position we essentially match its running time.

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