منابع مشابه
Covering by squares
In this paper we introduce the “do not touch” condition for squares in the discrete plane. We say that two squares “do not touch” if they do not share any vertex or any segment of an edge. Using this condition we define a covering of the discrete plane, the covering can be strong or weak, regular or non-regular. For simplicity, in this article, we will restrict our attention to regular covering...
متن کاملMaximal Covering by Two Isothetic Unit Squares
Let P be the point set in two dimensional plane. In this paper, we consider the problem of locating two isothetic unit squares such that together they cover maximum number of points of P . In case of overlapping, the points in their common zone are counted once. To solve the problem, we propose an algorithm that runs in O(n log n) time using O(n log n) space.
متن کاملCovering Points by Isothetic Unit Squares
Given a set P of n points in R, we consider two related problems. Firstly, we study the problem of computing two isothetic unit squares which may be either disjoint or intersecting (having empty common zone) such that they together cover maximum number of points. The time and space complexities of the proposed algorithm for this problem are both O(n). We also study the problem of computing k di...
متن کاملStrong covering without squares
The study of “covering lemmas” started with Jensen [DeJe] who proved in 1974–5 that in the absence of 0 there is a certain degree of resemblance between V and L. More precisely, if 0 does not exist then for every set of ordinals X there exists a set of ordinals Y ∈ L such that X ⊆ Y and V 2 |Y | = max{|X|,א1}. There is no hope of covering countable sets by countable ones in general, because doi...
متن کاملCovering Segments with Unit Squares
We study several variations of line segment covering problem with axis-parallel unit squares in IR. A set S of n line segments is given. The objective is to find the minimum number of axis-parallel unit squares which cover at least one end-point of each segment. The variations depend on the orientation and length of the input segments. We prove some of these problems to be NP-complete, and give...
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ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 2008
ISSN: 0304-3975
DOI: 10.1016/j.tcs.2007.10.044