Optimal Polygon Placement
نویسندگان
چکیده
Given a simple polygon P with m vertices and a set S of n points in the plane, we consider the problem of finding a rigid motion placement of P that contains the maximum number of points in S. We present two solutions to this problem that represent time versus space tradeoffs. The first algorithm runs in O(n3m3) expected time using O(n2m2) space. The second algorithm runs in O(n3m3 log(nm)) deterministic time and O(nm) space. While these algorithms represent a substantial improvement in the time bounds of previous work the main contribution is that the approach is extendible to related rigid motion placement problems including polygonal annulus placement.
منابع مشابه
Ooset-polygon Annulus Placement Problems ?
In this paper we address several variants of the polygon an-nulus placement problem: given an input polygon P and a set S of points, nd an optimal placement of P that maximizes the number of points in S that fall in a certain annulus region deened by P and some ooset distance > 0. We address the following variants of the problem: placement of a convex polygon as well as a simple polygon; placem...
متن کاملOptimal Polygon Placement by Translation1
Let M be an m-sided simple polygon and N be an n-sided polygon with holes. In this paper we consider the problem of computing the feasible region i.e., the set of all placements by translation of M so that M lies inside N without intersecting any hole. First we propose an O(mn 2) time algorithm for computing the feasible region for the case when M is a monotone polygon. Then we consider the gen...
متن کاملAlgorithms for Computing Grazing Area
We consider the problem of sweeping (or grazing) the inte-rior/exterior of a polygon by a exible rope whose one end point (anchor) is attached on the boundary of the polygon. We present a linear time algorithm to compute the grazing area inside a simple polygon. We show how to extend the algorithm for computing the internal grazing area, without increasing its time complexity, to compute the gr...
متن کاملIllumination with Orthogonal Floodlights ? (extended Abstract)
We provide the rst tight bound for covering a polygon with n vertices and h holes with vertex guards. In particular, we provide tight bounds for the number of oodlights, placed at vertices or on the boundary , suucient to illuminate the interior or the exterior of an orthogonal polygon with holes. Our results lead directly to simple linear, and thus optimal, algorithms for computing a covering ...
متن کاملThe Discrete Voronoi Game in a Simple Polygon
Let P be a simple polygon with m vertices and let U be a set of n points in P . We consider the points of U to be “users”. We consider a game with two players P1 and P2. In this game, P1 places a point facility inside P , after which P2 places another point facility inside P . We say that a user u ∈ U is served by its nearest facility, where distances are measured by the geodesic distance in P ...
متن کامل