• myGriffith
    • Staff portal
    • Contact Us⌄
      • Future student enquiries 1800 677 728
      • Current student enquiries 1800 154 055
      • International enquiries +61 7 3735 6425
      • General enquiries 07 3735 7111
      • Online enquiries
      • Staff phonebook
    View Item 
    •   Home
    • Griffith Theses
    • Theses - Higher Degree by Research
    • View Item
    • Home
    • Griffith Theses
    • Theses - Higher Degree by Research
    • View Item
    JavaScript is disabled for your browser. Some features of this site may not work without it.

    Browse

  • All of Griffith Research Online
    • Communities & Collections
    • Authors
    • By Issue Date
    • Titles
  • This Collection
    • Authors
    • By Issue Date
    • Titles
  • Statistics

  • Most Popular Items
  • Statistics by Country
  • Most Popular Authors
  • Support

  • Contact us
  • FAQs
  • Admin login

  • Login
  • The NP-Hardness of Covering Points with Lines, Paths and Tours and their Tractability with FPT-Algorithms

    Thumbnail
    View/Open
    Heednacram_2010_02Thesis.pdf (1.683Mb)
    Author(s)
    Heednacram, Apichat
    Primary Supervisor
    Estivill-Castro, Vladimir
    Suraweera, Francis
    Year published
    2010
    Metadata
    Show full item record
    Abstract
    Given a problem for which no polynomial-time algorithm is likely to exist, we investigate how to attack this seemingly intractable problem based on parameterized complexity theory. We study hard geometric problems, and show that they are xed-parameter tractable (FPT) given an instance and a parameter k. This allows the problems to be solved exactly, rather than approximately, in polynomial time in the size of the input and exponential time in the parameter. Although the parameterized approach is still young, in recent years, there have been many results published concerning graph problems and databases. However, not many ...
    View more >
    Given a problem for which no polynomial-time algorithm is likely to exist, we investigate how to attack this seemingly intractable problem based on parameterized complexity theory. We study hard geometric problems, and show that they are xed-parameter tractable (FPT) given an instance and a parameter k. This allows the problems to be solved exactly, rather than approximately, in polynomial time in the size of the input and exponential time in the parameter. Although the parameterized approach is still young, in recent years, there have been many results published concerning graph problems and databases. However, not many earlier results apply the parameterized approach in the eld of computational geometry. This thesis, therefore, focuses on geometric NP-hard problems. These problems are the Line Cover problem, the Rectilinear Line Cover problem in higher dimensions, the Rectilinear Minimum-Links Spanning Path problem in higher dimensions, the Rectilinear Hyper- plane Cover problem, the Minimum-Bends Traveling Salesman Prob- lem and the Rectilinear Minimum-Bends Traveling Salesman Prob- lem, in addition to some other variants of these problems. The Rectilinear Minimum-Links Spanning Path problem in higher dimensions and the Rectilinear Hyperplane Cover problem had been the subject of only conjectures about their intractability. Therefore, we present the NP-completeness proofs for these problems. After verifying their hardness, we use the xed-parameter approach to solve the two problems. We focus on solving the decision version of the problems, rather than solving the optimizations. However, with the Line Cover problem we demonstrate that it is not dicult to adapt algorithms for the decision version to algorithms for the optimization version. We also implement several algorithms for the Line Cover problem and conduct experimental evaluations of our algorithms with respect to previously known algorithms. For the remaining problems in the thesis, we will establish only the fundamental results. That is, we determine xed-parameter tractability of those problems.
    View less >
    Thesis Type
    Thesis (PhD Doctorate)
    Degree Program
    Doctor of Philosophy (PhD)
    School
    School of Information and Communication Technology
    DOI
    https://doi.org/10.25904/1912/1694
    Copyright Statement
    The author owns the copyright in this thesis, unless stated otherwise.
    Item Access Status
    Public
    Subject
    algorithm
    polynomial-time
    line cover
    rectilinear
    Publication URI
    http://hdl.handle.net/10072/367754
    Collection
    • Theses - Higher Degree by Research

    Footer

    Disclaimer

    • Privacy policy
    • Copyright matters
    • CRICOS Provider - 00233E

    Tagline

    • Gold Coast
    • Logan
    • Brisbane - Queensland, Australia
    First Peoples of Australia
    • Aboriginal
    • Torres Strait Islander