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

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

Abstract

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.

Original languageEnglish
Title of host publication19th International Symposium on Experimental Algorithms, SEA 2021
EditorsDavid Coudert, Emanuele Natale
PublisherSchloss Dagstuhl - Leibniz-Zentrum für Informatik
ISBN (Electronic)9783959771856
DOIs
Publication statusPublished - 1 Jun 2021
Event19th International Symposium on Experimental Algorithms, SEA 2021 - Virtual, Nice, France
Duration: 7 Jun 20219 Jun 2021

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume190
ISSN (Print)1868-8969

Conference

Conference19th International Symposium on Experimental Algorithms, SEA 2021
Country/TerritoryFrance
CityVirtual, Nice
Period7/06/219/06/21

Bibliographical note

Funding Information:
Funding Work at TU Braunschweig was partially supported under grant FE407/21-1, “Computational Geometry: Solving Hard Optimization Problems” (CG:SHOP).

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).

Keywords

  • Algorithm engineering
  • Angular metric
  • Approximation
  • Bottleneck
  • Complexity
  • Constraint programming
  • Energy
  • Graph scanning
  • Makespan
  • Mixed-integer programming

Fingerprint

Dive into the research topics of 'Minimum scan cover and variants - Theory and experiments'. Together they form a unique fingerprint.

Cite this