Department of Computer Science | Institute of Theoretical Computer Science | CADMO

Theory of Combinatorial Algorithms

Prof. Emo Welzl and Prof. Bernd Gärtner

Mittagsseminar (in cooperation with M. Ghaffari, A. Steger and B. Sudakov)

Mittagsseminar Talk Information

Date and Time: Thursday, October 27, 2016, 12:15 pm

Duration: 30 minutes

Location: CAB G51

Speaker: Antonis Thomas

Exponential paths for history-based pivot rules on abstract cubes

Inspired by the Simplex algorithm for Linear Programming, we look at the behavior of some pivot rules on abstract cubes. In particular, we are interested in history-based rules: At every vertex decide on which vertex to go next based on the history (path) thus far. Arguably, the most well-known such rule is Zadeh's. This algorithm keeps a history of how many times each direction has been used; then, at every step it chooses the least used improving direction. In this talk, I will show examples of a few of history-based rules and review what is known about their behavior. The main strategy and challenges for designing lower bounds for them will then be discussed. For a specific one, known as Cunningham's rule, I will demonstrate a construction that forces it to take an exponentially long path.

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