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• W2077159475 abstract "We consider the terrain navigation problem in a two-dimensional polygonal subdivision consisting of obstacles, “free” regions (in which one can travel at no cost), and regions in which cost is proportional to distance traveled. This problem is a special case of the weighted region problem and is a generalization of the well-known planar shortest path problem in the presence of obstacles. We present an Ο(n2) exact algorithm for this problem and faster algorithms for the cases of convex free regions and/or obstacles. We generalize our algorithm to allow arbitrary weights on the edges of the subdivision. In addition, we present algorithms to solve a variety of important applications: (1) an Ο(n2W) algorithm for finding lexicographically shortest paths in weighted regions (with W different weights); (2) an Ο(k2n2) algorithm for planning least-risk paths in a simple polygon that contains k line-of-sight threats (this becomes Ο(k4n4) in polygons with holes); and (3) an Ο(k2n3) algorithm for finding least-risk watchman routes in simple rectilinear polygons (a watchman route is such that each point in the polygon is visible from at least one point along the route)." @default.
• W2077159475 created "2016-06-24" @default.
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• W2077159475 date "1988-01-01" @default.
• W2077159475 modified "2023-10-18" @default.
• W2077159475 title "Path planning in 0/1/ weighted regions with applications" @default.
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• W2077159475 doi "https://doi.org/10.1145/73393.73421" @default.
• W2077159475 hasPublicationYear "1988" @default.
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