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  • The Rectilinear κ-Bends TSP

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    Author(s)
    Estivill-Castro, Vladimir
    Heednacram, Apichat
    Suraweera, Francis
    Griffith University Author(s)
    Suraweera, Francis
    Heednacram, Apichat
    Estivill-Castro, Vladimir
    Year published
    2010
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    Abstract
    We study a hard geometric problem. Given n points in the plane and a positive integer k, the Rectilinear k -Bends Traveling Salesman Problem asks if there is a piecewise linear tour through the n points with at most k bends where every line-segment in the path is either horizontal or vertical. The problem has applications in VLSI design. We prove that this problem belongs to the class FPT (fixed-parameter tractable). We give an algorithm that runs in O(kn 2?+?k 4k n) time by kernelization. We present two variations on the main result. These variations are derived from the distinction between line-segments and lines. ...
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    We study a hard geometric problem. Given n points in the plane and a positive integer k, the Rectilinear k -Bends Traveling Salesman Problem asks if there is a piecewise linear tour through the n points with at most k bends where every line-segment in the path is either horizontal or vertical. The problem has applications in VLSI design. We prove that this problem belongs to the class FPT (fixed-parameter tractable). We give an algorithm that runs in O(kn 2?+?k 4k n) time by kernelization. We present two variations on the main result. These variations are derived from the distinction between line-segments and lines. Note that a rectilinear tour with k bends is a cover with k line-segments, and therefore a cover by lines. We derive FPT-algorithms using bounded-search-tree techniques and improve the time complexity for these variants.
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    Journal Title
    Lecture Notes in Computer science
    Volume
    6196
    DOI
    https://doi.org/10.1007/978-3-642-14031-0_30
    Copyright Statement
    © 2010 Springer Berlin / Heidelberg. This is the author-manuscript version of this paper. Reproduced in accordance with the copyright policy of the publisher. The original publication is available at www.springerlink.com
    Subject
    Analysis of Algorithms and Complexity
    Publication URI
    http://hdl.handle.net/10072/34462
    Collection
    • Journal articles

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