A Pseudopolynomial Time O(logn)-Approximation Algorithm for Art Gallery Problems

  • Ajay Deshpande
  • Taejung Kim
  • Erik D. Demaine
  • Sanjay E. Sarma
Conference paper

DOI: 10.1007/978-3-540-73951-7_15

Part of the Lecture Notes in Computer Science book series (LNCS, volume 4619)
Cite this paper as:
Deshpande A., Kim T., Demaine E.D., Sarma S.E. (2007) A Pseudopolynomial Time O(logn)-Approximation Algorithm for Art Gallery Problems. In: Dehne F., Sack JR., Zeh N. (eds) Algorithms and Data Structures. WADS 2007. Lecture Notes in Computer Science, vol 4619. Springer, Berlin, Heidelberg

Abstract

In this paper, we give a O(logcopt)-approximation algorithm for the point guard problem where copt is the optimal number of guards. Our algorithm runs in time polynomial in n, the number of walls of the art gallery and the spread Δ, which is defined as the ratio between the longest and shortest pairwise distances. Our algorithm is pseudopolynomial in the sense that it is polynomial in the spread Δ as opposed to polylogarithmic in the spread Δ, which could be exponential in the number of bits required to represent the vertex positions. The special subdivision procedure in our algorithm finds a finite set of potential guard-locations such that the optimal solution to the art gallery problem where guards are restricted to this set is at most 3copt. We use a set cover cum VC-dimension based algorithm to solve this restricted problem approximately.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Ajay Deshpande
    • 1
  • Taejung Kim
    • 2
  • Erik D. Demaine
    • 1
  • Sanjay E. Sarma
    • 1
  1. 1.Massachusetts Institute of Technology, Cambridge, MA 02139USA
  2. 2.Dankook University, Hanam-Dong, Seoul, 140-714Korea

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