Minimum scan cover and variants - Theory and experiments

Kevin Buchin, Sándor P. Fekete, Alexander Hill, Linda Kleist, Irina Kostitsyna, Dominik Krupke, Roel Lambers, Martijn Struijs

Onderzoeksoutput: Hoofdstuk in Boek/Rapport/CongresprocedureConferentiebijdrageAcademicpeer review

Samenvatting

We consider a spectrum of geometric optimization problems motivated by contexts such as satellite communication and astrophysics. In the problem Minimum Scan Cover with Angular Costs, we are given a graph G that is embedded in Euclidean space. The edges of G need to be scanned, i.e., probed from both of their vertices. In order to scan their edge, two vertices need to face each other; changing the heading of a vertex incurs some cost in terms of energy or rotation time that is proportional to the corresponding rotation angle. Our goal is to compute schedules that minimize the following objective functions: (i) in Minimum Makespan Scan Cover (MSC-MS), this is the time until all edges are scanned; (ii) in Minimum Total Energy Scan Cover (MSC-TE), the sum of all rotation angles; (iii) in Minimum Bottleneck Energy Scan Cover (MSC-BE), the maximum total rotation angle at one vertex. Previous theoretical work on MSC-MS revealed a close connection to graph coloring and the cut cover problem, leading to hardness and approximability results. In this paper, we present polynomial-time algorithms for 1D instances of MSC-TE and MSC-BE, but NP-hardness proofs for bipartite 2D instances. For bipartite graphs in 2D, we also give 2-approximation algorithms for both MSC-TE and MSC-BE. Most importantly, we provide a comprehensive study of practical methods for all three problems. We compare three different mixed-integer programming and two constraint programming approaches, and show how to compute provably optimal solutions for geometric instances with up to 300 edges. Additionally, we compare the performance of different meta-heuristics for even larger instances.

Originele taal-2Engels
Titel19th International Symposium on Experimental Algorithms, SEA 2021
RedacteurenDavid Coudert, Emanuele Natale
UitgeverijSchloss Dagstuhl - Leibniz-Zentrum für Informatik
ISBN van elektronische versie9783959771856
DOI's
StatusGepubliceerd - 1 jun 2021
Evenement19th International Symposium on Experimental Algorithms, SEA 2021 - Virtual, Nice, Frankrijk
Duur: 7 jun 20219 jun 2021

Publicatie series

NaamLeibniz International Proceedings in Informatics, LIPIcs
Volume190
ISSN van geprinte versie1868-8969

Congres

Congres19th International Symposium on Experimental Algorithms, SEA 2021
Land/RegioFrankrijk
StadVirtual, Nice
Periode7/06/219/06/21

Bibliografische nota

Publisher Copyright:
© Kevin Buchin, Sándor P. Fekete, Alexander Hill, Linda Kleist, Irina Kostitsyna, Dominik Krupke, Roel Lambers, and Martijn Struijs; licensed under Creative Commons License CC-BY 4.0 19th International Symposium on Experimental Algorithms (SEA 2021).

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