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arXiv · 1504.07129

Scheduling Bidirectional Traffic on a Path

Yann Disser·Max Klimm·Elisabeth Lübbecke
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Abstract

We study the fundamental problem of scheduling bidirectional traffic along a path composed of multiple segments. The main feature of the problem is that jobs traveling in the same direction can be scheduled in quick succession on a segment, while jobs in opposing directions cannot cross a segment at the same time. We show that this tradeoff makes the problem significantly harder than the related flow shop problem, by proving that it is NP-hard even for identical jobs. We complement this result with a PTAS for a single segment and non-identical jobs. If we allow some pairs of jobs traveling in different directions to cross a segment concurrently, the problem becomes APX-hard even on a single segment and with identical jobs. We give polynomial algorithms for the setting with restricted compatibilities between jobs on a single and any constant number of segments, respectively.

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Yann Disser, Max Klimm, Elisabeth Lübbecke. 2015-04-27. Scheduling Bidirectional Traffic on a Path. https://arxiv.org/abs/1504.07129

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