Scheduling maintenance jobs in networks

Fidaa Abed, Lin Chen, Yann Disser, Martin Groß, Nicole Megow, Julie Meißner, Alexander T. Richter, Roman Rischke

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

We investigate the problem of scheduling the maintenance of edges in a network, motivated by the goal of minimizing outages in transportation or telecommunication networks. We focus on maintaining connectivity between two nodes over time; for the special case of path networks, this is related to the problem of minimizing the busy time of machines. We show that the problem can be solved in polynomial time in arbitrary networks if preemption is allowed. If preemption is restricted to integral time points, the problem is NP-hard and in the non-preemptive case we give strong non-approximability results. Furthermore, we give tight bounds on the power of preemption, that is, the maximum ratio of the values of non-preemptive and preemptive optimal solutions. Interestingly, the preemptive and the non-preemptive problem can be solved efficiently on paths, whereas we show that mixing both leads to a weakly NP-hard problem that allows for a simple 2-approximation.

Original languageEnglish
Pages (from-to)107-121
Number of pages15
JournalTheoretical Computer Science
Volume754
DOIs
StatePublished - Jan 6 2019

Keywords

  • Approximation algorithm
  • Complexity theory
  • Connectivity
  • Maintenance
  • Scheduling

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