Minimum Perimeter-Sum Partitions in the Plane
نویسندگان
چکیده
Let P be a set of n points in the plane. We consider the problem of partitioning P into two subsets P1 and P2 such that the sum of the perimeters of ch(P1) and ch(P2) is minimized, where ch(Pi) denotes the convex hull of Pi. The problem was first studied by Mitchell and Wynters in 1991 who gave an O(n2) time algorithm. Despite considerable progress on related problems, no subquadratic time algorithm for this problem was found so far. We present an exact algorithm solving the problem in O(n log4 n) time and a (1 + ε)-approximation algorithm running in O(n+ 1/ε2 · log4(1/ε)) time. 1998 ACM Subject Classification F.2.2 Nonnumerical Algorithms and Problems
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