Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

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

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Hung Hoang

ARRIVAL: Intermediate Stops

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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