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How to Keep an Eye on Small Things
Malmö University, Faculty of Technology and Society (TS), Department of Computer Science and Media Technology (DVMT).ORCID iD: 0000-0002-1342-8618
Institute of Informatics, University of Gdańsk, 80-308 Gdańsk, Poland.
2020 (English)In: International journal of computational geometry and applications, ISSN 0218-1959, Vol. 30, no 02, p. 97-120Article in journal (Refereed) Published
Abstract [en]

We present new results on two types of guarding problems for polygons. For the first problem, we present an optimal linear time algorithm for computing a smallest set of points that guard a given shortest path in a simple polygon having 𝑛n edges. We also prove that in polygons with holes, there is a constant 𝑐>0c>0 such that no polynomial-time algorithm can solve the problem within an approximation factor of 𝑐log𝑛clogn, unless P=NP. For the second problem, we present a (𝑘+ℎ)(k+h)-FPT algorithm for computing a shortest tour that sees 𝑘k specified points in a polygon with ℎh holes. We also present a 𝑘k-FPT approximation algorithm for this problem having approximation factor 2‾√2. In addition, we prove that the general problem cannot be polynomially approximated better than by a factor of 𝑐log𝑛clogn, for some constant 𝑐>0c>0, unless P=NP.

Place, publisher, year, edition, pages
World Scientific, 2020. Vol. 30, no 02, p. 97-120
Keywords [en]
Visibility, guarding, approximation algorithm, FPT-algorithm
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:mau:diva-56822DOI: 10.1142/s0218195920500053Scopus ID: 2-s2.0-85101295110OAI: oai:DiVA.org:mau-56822DiVA, id: diva2:1720771
Available from: 2022-12-20 Created: 2022-12-20 Last updated: 2024-02-05Bibliographically approved

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Nilsson, Bengt J.

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