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On the Approximability of Time Disjoint Walks

  • Alexandre Bayen
  • Jesse Goodman
  • Eugene Vinitsky
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11346)

Abstract

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 \(\varDelta \le 3\), Time Disjoint Walks is APX-hard. We also present a natural approximation algorithm, and provide a tight analysis. In particular, we prove that it achieves an approximation ratio of \(\varTheta (k/\log k)\) on bounded-degree DAGs, and \(\varTheta (k)\) on DAGs and bounded-degree digraphs.

Keywords

Hardness of approximation Approximation algorithms Disjoint Paths problem 

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Alexandre Bayen
    • 1
  • Jesse Goodman
    • 2
  • Eugene Vinitsky
    • 1
  1. 1.University of California, BerkeleyBerkeleyUSA
  2. 2.Cornell UniversityIthacaUSA

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