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

Date and Time: Thursday, October 23, 2014, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: May Szedlák

Combinatorial Redundancy Detection

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. The basic question is: What kind of information about the linear system do we need in order to detect all redundant halfspaces? We show that it is enough to know the finitely many dictionaries of H. A dictionary is a matrix that can be thought of as an enriched version of an intersection point of d halfspaces of H. It is enough if the dictionaries are given in a combinatorial setting, containing only signs and in particular no numerical values.

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