TY - GEN

T1 - On the approximability of time disjoint walks

AU - Bayen, Alexandre

AU - Goodman, Jesse

AU - Vinitsky, Eugene

N1 - Publisher Copyright:
© 2018, Springer Nature Switzerland AG.

PY - 2018

Y1 - 2018

N2 - We introduce the combinatorial optimization problem Time Disjoint Walks. This problem takes as input a digraph G with positive integer arc lengths, and k pairs of vertices that each represent a trip demand from a source to a destination. The goal is to find a path and delay for each demand so that no two trips occupy the same vertex at the same time, and so that the sum of trip times is minimized. We show that even for DAGs with max degree Δ ≤ 3, Time Disjoint Walks is APXhard. We also present a natural approximation algorithm, and provide a tight analysis. In particular, we prove that it achieves an approximation ratio of Θ(k/log k) on bounded-degree DAGs, and Θ(k) on DAGs and bounded-degree digraphs.

AB - We introduce the combinatorial optimization problem Time Disjoint Walks. This problem takes as input a digraph G with positive integer arc lengths, and k pairs of vertices that each represent a trip demand from a source to a destination. The goal is to find a path and delay for each demand so that no two trips occupy the same vertex at the same time, and so that the sum of trip times is minimized. We show that even for DAGs with max degree Δ ≤ 3, Time Disjoint Walks is APXhard. We also present a natural approximation algorithm, and provide a tight analysis. In particular, we prove that it achieves an approximation ratio of Θ(k/log k) on bounded-degree DAGs, and Θ(k) on DAGs and bounded-degree digraphs.

KW - Approximation algorithms

KW - Disjoint Paths problem

KW - Hardness of approximation

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U2 - 10.1007/978-3-030-04651-4_5

DO - 10.1007/978-3-030-04651-4_5

M3 - Conference contribution

AN - SCOPUS:85058529059

SN - 9783030046507

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 62

EP - 78

BT - Combinatorial Optimization and Applications - 12th International Conference, COCOA 2018, Proceedings

A2 - Zelikovsky, Alexander

A2 - Kim, Donghyun

A2 - Uma, R.N.

PB - Springer Verlag

T2 - 12th Annual International Conference on Combinatorial Optimization and Applications, COCOA 2018

Y2 - 15 December 2018 through 17 December 2018

ER -