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

Date and Time: Thursday, July 18, 2013, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Julia Pap

Complexity of Hilbert bases, TDL-ness and g-polymatroids

A usual type of question in combinatorial optimization is to give the defining linear system of a certain class of combinatorially defined polytopes. The properties of the defining linear system tell us a lot about the tractability and structure of the problem. In my talk we consider questions from a different point of view: given a linear system can we decide whether it has a certain nice property?

We examine several properties of polyhedra from this computational point of view. First we consider total dual integrality and the related notion of Hilbert bases, which turn out to be co-NP-complete. On the other hand, it can be decided in polynomial time whether a system describes a generalized polymatroid, which is a broad class of "tractable" polyhedra. A related notion that we call total dual laminarity is in contrast NP-hard.

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