Efficient RMESH Algorithms for Computing the Intersection and the Union of Two Visibility Polygons

- Journal title : Journal of the Korea Institute of Information and Communication Engineering
- Volume 20, Issue 2, 2016, pp.401-407
- Publisher : The Korean Institute of Information and Commucation Engineering
- DOI : 10.6109/jkiice.2016.20.2.401

Title & Authors

Efficient RMESH Algorithms for Computing the Intersection and the Union of Two Visibility Polygons

Kim, Soo-Hwan;

Kim, Soo-Hwan;

Abstract

We can consider the following problems for two given points p and q in a simple polygon P. (1) Compute the set of points of P which are visible from both p and q. (2) Compute the set of points of P which are visible from either p or q. They are corresponding to the problems which are to compute the intersection and the union of two visibility polygons. In this paper, we consider algorithms for solving these problems on a reconfigurable mesh(in short, RMESH). The algorithm in [1] can compute the intersection of two general polygons in constant time on an RMESH with size O(), where n is the total number of vertices of two polygons. In this paper, we construct the planar subdivision graph in constant time on an RMESH with size O() using the properties of the visibility polygon for preprocessing. Then we present O() time algorithms for computing the union as well as the intersection of two visibility polygons, which improve the processor-time product from O() to O().

Keywords

parallel algorithm;reconfigurable mesh;visibility polygon;planar subdivision;

Language

Korean

References

1.

R. Miller, V. K. Prasanner Kumar, D. Reisis, and Q.Stout, "Meshes with Reconfigurable Buses," in Proceeding of 5th MIT Conf. on Adv. Res. in VLSI, pp. 163-178, March 1988.

2.

R. Wankar and R. Akerkar, "Reconfigurable architectures and algorithms: a research survey," International Journal of Computer Science and Applications, vol. 6, no. 1, pp. 108-123, Jan. 2009.

3.

T. Pan, "The transitive closure and related algorithms of digraph on the reconfigurable architecture," Parallel Processing Letters, vol. 21, no. 1, pp. 27-43, March 2011.

4.

O. Bouattane, B. Cherradi, M. Youssfi, M. O. Bensalah, "Paralle c-means algorithm for image segmentation on a reconfigurable mesh computer," Parallel Computing, vol. 37, pp. 230-243, April-May 2011.

5.

D. T. Lee, "Visibility of a simple polygon," Computer Vision, Graphics, and Image Processing, vol. 22, pp. 207-221, May 1983.

6.

H.-G. Kim and Y.-K. Cho, "Point Visibility of a Simple Polygon on Reconfigurable Mesh," in Proceeding of 5 th IEEE Symposium on Parallel and Distributed Processing, pp. 748-751, Dec. 1993.

7.

S. H, Kim, "Optimal algorithms for the Set operations of two visibility polygons in a simple polygon," Journal of KISS: Computer Systems and Theory, vol. 31, no. 1-2, pp. 102-111, Feb. 2004.

8.

S. H. Kim, "Constant time RMESH algorithms for polygon intersection problems," Journal of KISS: Computer Systems and Theory, vol. 26, no. 11, pp. 1344-1352, Nov. 1999.

9.

S. G. Akl, The Design and Analysis of Parallel Algorithms, Prentice-Hall, Inc., Upper Saddle River, NJ, 1989.

10.

S. H. Kim, "An efficient RMESH algorithms for finding a cycle vertex sequence from the edge set of a directed cycle graph," Journal of KIISE: Computer Systems and Theory, vol. 41, no. 3, pp. 146-150, Jun 2014.