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

Prof. Emo Welzl and Prof. Bernd Gärtner

Mittagsseminar Talk Information |

**Date and Time**: Thursday, February 28, 2019, 12:15 pm

**Duration**: 30 minutes

**Location**: CAB G51

**Speaker**: Hung Hoang

Suppose we run a train on a directed (multi-)graph, where every vertex has out-degree 2 and is equipped with a switch. At the beginning, the switch at each vertex points to one of the two outgoing edges. When the train reaches a vertex, it will traverse along the edge pointed by the switch, and then the switch at that vertex shifts to the other outgoing edge. Given such a graph with an origin vertex *o* and a destination vertex *d*, the problem is to decide if the train starting from *o* can reach *d*.

The problem above is called ARRIVAL. It is known that the problem is in NP and co-NP. The open question is whether it is in P. In this talk, I will present a combinatorial algorithm that runs in time O(2^(n/2)) and a polynomial time algorithm for a subclass of the problem. The latter is by modelling the problem as an integer programme and examining the primal and dual of the linear relaxation.

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