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

Date and Time: Tuesday, April 23, 2024, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Raphael Steiner

Short paths on and diameters of polytopes

In this talk I will present some of my results regarding the computational complexity of computing/approximating shortest paths on polytopes, as well as computing diameters of polytopes. The first result (joint with Jean Cardinal) shows that shortest paths on perfect matching polytopes are not approximable to within any constant factor, unless P=NP, and not to within a factor of Theta(log d/log log d), where d is the dimension of the polytope, unless ETH fails. This answers a question by de Loera et al. and disproves a conjecture of Ito et al. The second result (joint with Christian Nöbel) is that computing the combinatorial diameter of perfect matching polytopes, as well as several versions of diameter, are NP-hard. This strengthens a result by Sanita and solves a problem posed by Borgwardt et al.

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