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A Robust and Fast Algorithm for Computing Exact and Approximate Shortest Visiting Routes

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Computational Science and Its Applications – ICCSA 2004 (ICCSA 2004)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3045))

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Abstract

Given a simple n-sided polygon in the plane with a boundary partitioned into subchains some of which are convex and colored, we consider the following problem: Which is the shortest route (closed path) contained in the polygon that passes through a given point on the boundary and intersects at least one vertex in each of the colored subchains? We present an optimal algorithm that solves this problem in O(n) time. Previously it was known how to solve the problem optimally when each colored subchain contains one vertex only. Moreover, we show that a solution computed by the algorithm is at most a factor \(\frac{2+c}{c}\) times longer than the overall shortest route that intersects the subchains (not just at vertices) if the minimal distance between vertices of different subchains is at least c times the maximal length of an edge of a subchain. Without such a bound its length can be arbitrarily longer. Furthermore, it is known that algorithms for computing such overall shortest routes suffer from numerical problems. Our algorithm is not subject to such problems.

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Author information

Authors and Affiliations

  1. Department of Computer Science and Electrical Engineering, Luleå University of Technology, SE-971 87, Luleå, Sweden

    Håkan Jonsson

Authors
  1. Håkan Jonsson
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Editor information

Editors and Affiliations

  1. Department of Chemistry, University of Perugia, Via Elce di Sotto, 8, I-06123, Perugia, Italy

    Antonio Laganá

  2. Department of Computer Science, University of Calgary, 2500 University Drive N.W., T2N 1N4, Calgary, AB, Canada

    Marina L. Gavrilova

  3. William Norris Professor, Head of the Computer Science and Engineering Department, University of Minnesota, USA

    Vipin Kumar

  4. School of Computing, Soongsil University, Seoul, Korea

    Youngsong Mun

  5. OptimaNumerics Ltd., Cathedral House, 23-31 Waring Street, BT1 2DX, Belfast, UK

    C. J. Kenneth Tan

  6. Department of Mathematics and Computer Science, University of Perugia, via Vanvitelli, 1, I-06123, Perugia, Italy

    Osvaldo Gervasi

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© 2004 Springer-Verlag Berlin Heidelberg

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Jonsson, H. (2004). A Robust and Fast Algorithm for Computing Exact and Approximate Shortest Visiting Routes. In: Laganá, A., Gavrilova, M.L., Kumar, V., Mun, Y., Tan, C.J.K., Gervasi, O. (eds) Computational Science and Its Applications – ICCSA 2004. ICCSA 2004. Lecture Notes in Computer Science, vol 3045. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24767-8_18

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  • DOI: https://doi.org/10.1007/978-3-540-24767-8_18

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-22057-2

  • Online ISBN: 978-3-540-24767-8

  • eBook Packages: Springer Book Archive

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