Y. Ke
ABSTRACT
The link distance between two points inside a simple polygon P is defined to be the minimum number of edges required to form a polygonal path inside P that connects the points. A link furthest neighbor of a point p Ε P is a point of P whose link distance is the maximum from p. The link center of P is the collection of points whose link distances to their link furthest neighbors are minimized. We present an Ο(n log n) time and Ο(n) space algorithm for computing the link center of a simple polygon P, where n is the number of vertices of P. This improves the previous Ο(n2) time and space algorithm. Our algorithm essentially sweeps a chord through the polygon and spends Ο(log n) time at each step. We demonstrate that the output of the algorithm, a sequence of sets of chords, is a powerful tool for solving several other link distance problems.
- 1.B. Chazelle and L. Guibas. Visibility and intersection problems in plane geometry. In Proc. of First ACM Symposium on Computational Geometry, pages 135-146, 1985. Google Scholar
Digital Library
- 2.H. N. Djidjev, A. Lingas, and J.-R. Sack. An O(n log n) Algorithm for Computing a Link Center in a Simple Polygon. Technical Report SCS- TR-148, School of Computer Science, Carleton Universily, 1988.Google Scholar
- 3.H. Edelsbrunner, L. Guibas, and J. Stolfi. Optimal point location in monotone subdivisions. SIAM Journal on Computing, 15(2):317-340, 1986. Google ScholarDigital Library
- 4.L. Guibas and J. Hershberger. Optimal shortest path queries in a simple polygon. In Proc. of Third ACM Symposium on Computational Geometry, pages 50-63, 1987. Google ScholarDigital Library
- 5.L. Guibas, J. Hershberger, D. Leven, M. Sharir, and R. Tarjan. Linear time algorithms for visibility and shortest path problems inside simple polygons. In Proceedings of the second ACM Symposium on Computational Geometry, pages 1-13, 1986. Google ScholarDigital Library
- 6.Y. Ke. An Efficient Algorithm for Link Distance Problems inside a Simple Polygon. Technical Report 28, Department of Computer Science, The Johns Hopkins University, 1987.Google Scholar
- 7.Y. Ke. Efficient Algorithms for Weak Visibility and Link Distance Problems in Polygons. PhD thesis, The Johns Hopkins University, spring 1989. Google ScholarDigital Library
- 8.Y. Ke. Testing the Weak Visibility of a Simple Polygon and Related Problems. Technical Report 27, Department of Computer Science, The Johus Hopkins University, 1987.Google Scholar
- 9.Y. Ke and J. O'Rourke. Weak Visibility Problems for a Set of Points in a Simple Polygon. Technical Report, Department of Computer Science, The Johns Hopkins University, 1987.Google Scholar
- 10.W. Lenhart, R. Pollack, J. Sack, R. Seidel, M. Sharir, S. Suri, S. Whitesides G. Toussaint, and C. Yap. Computing the link center of a simple polygon. In Proceedings of the third ACM Symposium on Computational Geometry, pages 1-10, 1987. Google ScholarDigital Library
- 11.D. Johnson M. Garey, F. Preparata, and R. Tarjan. Triangulating a simple polygon. Information Processing Letters, 7(4):175-180, 1978.Google ScholarCross Ref
- 12.S. Suri. A linear time algorithm for minimum link paths inside a simple polygon. Computer Vision, Graphics and Image Processing, 35, 1986. Google ScholarDigital Library
- 13.S. Suri. Minimum Link Paths in Polygons and Related Problems. PhD thesis, The Johns Hopkins University, August 1987. Google ScholarDigital Library
- 14.R. Tarjan and C. Van Wyk. An o(n log n log n) time algorithm for triangulating simple polygons. preprint (to appear in SIAM Journal on Computing), 1986. Google ScholarDigital Library
Index Terms
- An efficient algorithm for link-distance problems
Recommendations
Parallel algorithms for rectilinear link distance problems
IPPS '93: Proceedings of the 1993 Seventh International Parallel Processing SymposiumThe authors provide optimal parallel solutions to several fundamental link distance problems set in trapezoided rectilinear polygons. All parallel algorithms are deterministic, run in logarithmic time, have an optimal time-processor product and are ...
Optimal parallel algorithms for rectilinear link-distance problems
We provide optimal parallel solutions to several link-distance problems set in trapezoided rectilinear polygons. All our main parallel algorithms are deterministic and designed to run on the exclusive read exclusive write parallel random access machine (...
Comments