منابع مشابه
Minimum-perimeter enclosures
We give the first polynomial-time algorithm for the problem of finding a minimumperimeter k-gon that encloses a given n-gon. Our algorithm is based on a simple structural result, that an optimal k-gon has at least one “flush” edge with the ngon. This allows one to reduce the problem to computing the shortest k-link path in a simple polygon. As a by-product we observe that the minimum-perimeter ...
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The number of essentially different square polyominoes of order n and minimum perimeter p(n) is enumerated.
متن کاملMinimum-Perimeter Enclosing k-gon
Introduction Let P = p1, . . . , pn be a simple polygon (all polygons are assumed convex throughout this paper). A fundamental problem in geometric optimization is to compute a minimum-area or a minimum-perimeter convex k-gon (denoted QA or Qp, resp.) that encloses P . While efficient algorithms for finding QA are known for more than 20 years [8, 1, 2], the problem of finding Qp has remained op...
متن کاملAdding Layers to Bumped-Body Polyforms with Minimum Perimeter Preserves Minimum Perimeter
In two dimensions, a polyform is a finite set of edge-connected cells on a square, triangular, or hexagonal grid. A layer is the set of grid cells that are vertex-adjacent to the polyform and not part of the polyform. A bumped-body polyform has two parts: a body and a bump. Adding a layer to a bumped-body polyform with minimum perimeter constructs a bumped-body polyform with min perimeter; the ...
متن کاملMinimum Perimeter-Sum Partitions in the Plane
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 algo...
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ژورنال
عنوان ژورنال: Mathematical Programming
سال: 1997
ISSN: 0025-5610,1436-4646
DOI: 10.1007/bf02614375