Distance-based solution of patrolling problems with individual waiting times
Paper i proceeding, 2021

In patrolling problems, robots (or other vehicles) must perpetually visit certain points without exceeding given individual waiting times. Some obvious applications are monitoring, maintenance, and periodic fetching of resources. We propose a new generic formulation of the problem. As its main advantage, it enables a reduction of the multi-robot case to the one-robot case in a certain graph/hypergraph pair, which also relates the problem to some classic path problems in graphs: NP-hardness is shown by a reduction from the Hamiltonian cycle problem, and on the positive side, the formulation allows solution heuristics using distances in the mentioned graph. We demonstrate this approach for the case of two robots patrolling on a line, a problem whose complexity status is open, apart from approximation results. Specifically, we solve all instances with up to 6 equidistant points, and we find some surprising effects, e.g., critical problem instances (which are feasible instances that become infeasible when any waiting time is diminished) may contain rather large individual waiting times.

periodic scheduling

shortest path

patrolling

well-quasi ordering

Författare

Peter Damaschke

Data Science och AI

OASIcs

2190-6807 (ISSN)

Vol. 96 14

21st Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems, ATMOS 2021
Lisbon, Portugal,

Fundament

Grundläggande vetenskaper

Ämneskategorier

Diskret matematik

DOI

10.4230/OASIcs.ATMOS.2021.14

ISBN

9783959772136

Mer information

Senast uppdaterat

2021-11-11