Abstract
We show that it is possible to find a diagonal partition of anyn-vertex simple polygon into smaller polygons, each of at mostm edges, minimizing the total length of the partitioning diagonals, in timeO(n 3 m 2). We derive the same asymptotic upper time-bound for minimum length diagonal partitions of simple polygons into exactlym-gons provided that the input polygon can be partitioned intom-gons. Also, in the latter case, if the input polygon is convex, we can reduce the upper time-bound toO(n 3 logm).
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References
L. Gotlieb,Optimal multi-way search trees, SIAM J. Comput., vol. 10 (1981), No. 3.
A. Itai,Optimal alphabetic trees, SIAM J. Comput., vol. 5 (1976), pp. 9–18.
J. M. Keil and J. R. Sack,Minimum decompositions of polygonal objects, inComputational Geometry. Edited by G. T. Toussaint. North-Holland, Amsterdam, The Netherlands, 1985.
G. T. Klincsek,Minimal triangulations of polygonal domains, Ann. Discrete Math., vol. 9 (1980), pp. 121–123.
D. T. Lee,Visibility of a simple polygon, Computer Vision, Graphics, and Image Processing, Vol. 22 (1983), pp. 207–221.
A. Lingas,The greedy and Delaunay triangulations are not bad in the average case, Information Processing Letters, vol. 22 (1986), pp. 25–31.
G. Strang and G. Fich,An Analysis of the Finite Element Method, Prentice-Hall, Englewood Cliffs, NJ, 1973.
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Lingas, A., Levcopoulos, C. & Sack, J. Algorithms for minimum length partitions of polygons. BIT 27, 474–479 (1987). https://doi.org/10.1007/BF01937272
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DOI: https://doi.org/10.1007/BF01937272