Packing Boundary-Anchored Rectangles
نویسندگان
چکیده
In this paper, we study the boundary-anchored rectangle packing problem in which we are given a set P of points on the boundary of an axis-aligned squareQ. The goal is to find a set of disjoint axis-aligned rectangles in Q such that each rectangle is anchored at some point in P , each point in P is used to anchor at most one rectangle, and the total area of the rectangles is maximized. We show how to solve this problem in linear-time in the number of points of P , provided that the points of P are given in sorted order along the boundary of Q. The solvability of the general version of this problem, in which the points of P can also lie in the interior of Q, in polynomial-time, is still open.
منابع مشابه
Anchored Rectangle and Square Packings
For points p1, . . . , pn in the unit square [0, 1] , an anchored rectangle packing consists of interior-disjoint axis-aligned empty rectangles r1, . . . , rn ⊆ [0, 1] such that point pi is a corner of the rectangle ri (that is, ri is anchored at pi) for i = 1, . . . , n. We show that for every set of n points in [0, 1], there is an anchored rectangle packing of area at least 7/12 − O(1/n), and...
متن کاملOn Packing Almost Half of a Square with Anchored Rectangles: A Constructive Approach
In this paper, we consider the following geometric puzzle whose origin was traced to Allan Freedman [13, 22] in the 1960s by Dumitrescu and Tóth [10]. The puzzle has been popularized of late by Peter Winkler [23]. Let Pn be a set of n points, including the origin, in the unit square U = [0, 1] . The problem is to construct n axis-parallel and mutually disjoint rectangles inside U such that the ...
متن کاملPacking anchored rectangles
Let S be a set of n points in the unit square [0, 1], one of which is the origin. We construct n pairwise interior-disjoint axis-aligned empty rectangles such that the lower left corner of each rectangle is a point in S, and the rectangles jointly cover at least a positive constant area (about 0.09). This is a first step towards the solution of a longstanding conjecture that the rectangles in s...
متن کاملA THEORETICALLY CORRECT RESOURCE USAGE VISUALIZATION FOR THE RESOURCE-CONSTRAINED PROJECT SCHEDULING PROBLEM
The cumulative resource constraints of the resource-constrained project scheduling problem (RCPSP) do not treat the resource demands as geometric rectangles, that is, activities are not necessarily assigned to the same resource units over their processing times. In spite of this fact, most papers on resource-constrained project scheduling mainly in the motivation phase use a strip packing of re...
متن کاملThe structure of optimal partitions of orthogonal polygons into fat rectangles
Motivated by a VLSI masking problem, we explore partitions of an orthogonal polygon of n vertices into isothetic rectangles that maximize the shortest rectangle side over all rectangles. Thus no rectangle is “thin”; all rectangles are “fat.” We show that such partitions have a rich structure, more complex than what one might at first expect. For example, for partitions all “cuts” of which are a...
متن کامل