Oberseminar Discrete Optimization

On the Approximability of Train Routing and the MinMax Disjoint Paths ProblemOberseminar Discrete Optimization

by Britta Peis (RWTH Aachen University)

Europe/Berlin
Arithmeum, Lennéstr., 2 - Seminarraum (Arithmeum / Research Institute for Discrete Mathematics)

Arithmeum, Lennéstr., 2 - Seminarraum

Arithmeum / Research Institute for Discrete Mathematics

100
Description

In train routing, the headway is the minimum distance that must be maintained between successive trains for safety and robustness. We introduce a model for train routing that requires a fixed headway to be maintained between trains, and study the problem of minimizing the makespan, i.e., the arrival time of the last train, in a single-source single-sink network. For this problem, we first show that there exists an optimal solution where trains move in convoys---that is, the optimal paths for any two trains are either the same or are arc-disjoint.

Via this insight, we are able to reduce the approximability of our train routing problem to that of the min-max disjoint paths problem, which asks for a collection of disjoint paths where the maximum length of any path in the collection is as small as possible.

While min-max disjoint paths inherits a strong inapproximability result on directed acyclic graphs from the multi-level bottleneck assignment problem, we show that a natural greedy composition approach yields a logarithmic approximation in the number of disjoint paths for series-parallel graphs.

We also present an alternative analysis of this approach that yields a guarantee depending on how often the decomposition tree of the series-parallel graph alternates between series and parallel compositions on any root-leaf path.

Joint work with Umang Bhaskar, Katharina Eickhoff, Lennart Kauther, Jannik Matuschke and Laura Vargas Koch

 

The Oberseminar takes place in the Seminarraum, 1st floor. Participants are invited to have coffee or tea in the lounge before.

 

Organized by

S. Held, S. Hougardy, L. Végh, J. Vygen