Efficient computation of rectilinear geodesic voronoi neighbor in presence of obstacles

  • Pinaki Mitra
  • Subhas C. Nandy
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1180)


In this paper, we present an algorithm to compute the rectilinear geodesic voronoi neighbor of an arbitrary query point q among a set S of m points in the presence of a set O of n vertical line segment obstacles inside a rectangular floor. The distance between a pair of points α and Β is the shortest rectilinear distance avoiding the obstacles in O and is denoted by δ(α,Β). The rectilinear geodesic voronoi neighbor of an arbitrary query point q, (RGVN(q)) is the point p i S such that δ(q,p i ) is minimum. The algorithm suggests a preprocessing of the elements of the set S and O in O((m+n)log(m+n)) time such that for any arbitrary query point q, the RGVN query can be answered in O(max(logm, logn)) time. The space required for storing the preprocessed information is O(n+mlogm). If the points in S are placed on the boundary of the rectangular floor, a different technique is adopted to decrease the space complexity to O(m+n). The latter algorithm works even when the obstacles are rectangles instead of line segments.


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  1. [1]
    P. J. de Rezende, D. T. Lee and Y. F. Wu, Rectilinear shortest paths with rectangular barrier, Discrete Computational Geometry, vol. 4, 1989, pp. 41–53.Google Scholar
  2. [2]
    H. Elgindy and P. Mitra, Orthogonal shortest path queries among axes parallel rectangular obstacles, International Journal of Computational Geometry and Applications, 1994.Google Scholar
  3. [3]
    S. Guha and I. Suzuki, Proximity problems for points on rectilinear plane with rectangular obstacles, Proc. FST & TCS — 13, Lecture Notes in Computer Science, 1993, pp. 218–227.Google Scholar
  4. [4]
    D. B. Johnson, Efficient algorithms for shortest paths in sparse network, Journal of the Association of Computing Machinery, 1977, pp. 1–13.Google Scholar
  5. [5]
    D. G. Kirkpatrick, Optimal search in planar subdivision, SIAM Journal on Computing, vol. 12, 1983, pp. 28–35.Google Scholar
  6. [6]
    K. Mehlhorn, A faster approximation algorithm for the steiner problems in graphs, Information Processing Letters, vol. 27, 1988, pp. 125–128.Google Scholar
  7. [7]
    J. S. B. Mitchell, L 1 L shortest paths among polygonal obstacles in the plane, Algorithmica, vol. 8, 1992, pp. 55–88.Google Scholar
  8. [8]
    F. P. Preparata and M. I. Shamos, Computational Geometry — an Introduction, Springer-Verlag, New York, 1985.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Pinaki Mitra
    • 1
  • Subhas C. Nandy
    • 2
  1. 1.Dept. CSEJadavpur UniversityCalcuttaIndia
  2. 2.Indian Statistical InstituteCalcuttaIndia

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