Approxiamte Shortest Homotopic Paths in Weighted Regions∗
نویسندگان
چکیده
Let P be a path between two points s and t in a polygonal subdivision T with obstacles and weighted regions. Given a relative error tolerance ε ∈ (0, 1), we present the first algorithm to compute a path between s and t that can be deformed to P without passing over any obstacle and the path cost is within a factor 1 + ε of the optimum. The running time is O( 3 ε2 kn polylog(k, n, 1 ε )), where k is the number of segments in P and h and n are the numbers of obstacles and vertices in T , respectively. The constant in the running time of our algorithm depends on some geometric parameters and the ratio of the maximum region weight to the minimum region weight.
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