Abstract
We consider the problem of finding a shortest watchman route from which the exterior of a polygon is visible (external watchman route). We present an O (n 4 log logn) algorithm to find shortest external watchman routes for simple polygons by transforming the external watchman route problem to a set of internal watchman route problems. Also, we present faster external watchman route algorithms for special cases. These include optimal O (n) algorithms for convex, monotone, star and spiral polygons and an O (n log logn) algorithm for rectilinear polygons.
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References
Agarwal PK, Aggarwal A, Aronov B, Kosaraju SR, Schieber B, Suri S (1991) Computing external farthest neighbors for a simple polygon. Discrete Appl Math 31: 97–111
Asano T, Asano T, Guibas L, Hershberger J, Imai H (1985) Visibility polygon search and euclidean shortest paths. In: Proceedings of the 1985 FOCS. IEEE Computer Society Press, Washington DC, pp 155–164
Avis D, Toussaint G (1981) an optimal algorithm for determining the visibility, of a polygon from an edge. IEEE Trans Comput, Vol C-30, no 12 pp 910–914
Bhattacharya B, Kirkpatrick D, Toussaint G (1989) Determining sector visibility of a polygon. Proceedings of the 5th ACM Symposium on Computational Geometry. ACM Press, Baldimore, pp 247–253
Chin WP, Ntafos S (1988) Optimum watchman routes. Inf Process Lett 28: 39–44
Chin WP, Ntafos S (1991) Watchman routes in simple polygons. Discrete Comput Geom 6: 9–31
Edelsbrunner H, Overmars M, Wood D (1983) Graphics in flatland. In: Preparata F (ed) Advances in computing research: computational geometry. JAI Press, Greenwich, CN, 1: 35–59
Ghosh SK, Mount DM (1991) An output-sensitive algorithm for computing visibility graphs. SIAM J Comput 20: 888–910
Guibas L, Hershberger J, Leven D, Sharir M, Tarjan R (1986) Linear time algorithms for shortest paths and visibility inside simple polygons. In: Proceedings of the 2nd ACM Symposium on Computational Geometry. ACM Press, Baldimore, pp 1–13
Lee DT, Preparata F (1984) Euclidean shortest paths in the presence of rectilinear barriers. Networks 14: 393–410
Nilsson B, Wood D (1989) Optimum watchmen routes in spiral polygons, Proc. 2nd Conf. Comput Geom. The University of Ottawa, Canada, pp 269–272
O'Rourke J (1987) Art gallery theorems and algorithms. Oxford University Press, Oxford
Preparata F, Shamos M (1985) Computational geometry: an introduction. Springer, Berlin Heidelberg New York
Toussaint G, Avis D (1982) On a convex hull algorithm for polygons and its applications to triangulation problems. Patt Recogn 15 (1): 23–29
Wetzl E (1985) Constructing the visibility graph forn line segments in O(n 2) time. Inf Process Lett 20: 167–171
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This work was supported in part by a grant from Texas Instruments, Inc. to S. Ntafos
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Ntafos, S., Gewali, L. External watchman routes. The Visual Computer 10, 474–483 (1994). https://doi.org/10.1007/BF01910637
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DOI: https://doi.org/10.1007/BF01910637