## 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 15, 2015, 12:15 pm

Duration: 30 minutes

Location: CAB G51

Speaker: Antonis Thomas

## Unique Sink Orientations on the Grid

Consider the planar $(m,n)$-grid, which is the Cartesian product of the complete graphs $K_m$ and $K_n$. Our interest lies on Unique Sink Orientations of the corresponding digraph. This means that every non-trivial subgrid of our grid has a unique sink. This model has been introduced by Gärtner et al.,2001 and has been studied in a series of papers between 2001-2008.

We are interested in the vertex query model, where a vertex query reveals the orientation of all its incident edges. Let $M = \max\{m,n\}$. The fastest known (randomized) algorithm needs $O(\log^2 M)$ vertex queries in expectation. We investigate the existence of efficient deterministic algorithms. Towards this, we provide a linear lower bound and, our main contribution, a deterministic algorithm that finds the sink using $O(M \log M)$ vertex queries.

Joint work with Luis Barba, Malte Milatz and Jerri Nummenpalo

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