Approximation Algorithms for Rectangle Stabbing and Interval Stabbing Problems
نویسندگان
چکیده
منابع مشابه
Approximation Algorithms for Rectangle Stabbing and Interval Stabbing Problems
In the weighted rectangle stabbing problem we are given a grid in ]R2 consisting of columns and rows each having a positive integral weight, and a set of closed axis-parallel rectangles each having a positive integral demand. The rectangles are placed arbitrarily in the grid with the only assumption that each rectangle is intersected by at least one column and at least one row. The objective is...
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In the rectangle stabbing problem we are given a set of axis parallel rectangles and a set of horizontal and vertical lines, and our goal is to find a minimum size subset of lines that intersect all the rectangles. In this paper we study the capacitated version of this problem in which the input includes an integral capacity for each line. The capacity of a line bounds the number of rectangles ...
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Given a permutation π of {1, . . . , n} and a positive integer k, we give an algorithm with running time 2 2 log n that decides whether π can be partitioned into at most k increasing or decreasing subsequences. Thus we resolve affirmatively the open question of whether the problem is fixed parameter tractable. This NP-complete problem is equivalent to deciding whether the cochromatic number, pa...
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Given a set I of n intervals, a stabbing query consists of a point q and asks for all intervals in I that contain q. The Interval Stabbing Problem is to find a data structure that can handle stabbing queries efficiently. We propose a new, simple and optimal approach for different kinds of interval stabbing problems in a static setting where the query points and interval ends are in {1, . . . , ...
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We provide constant ratio approximation algorithms for two NP-hard problems, the rectangle stabbing problem and the rectilinear partitioning problem. In the rectangle stabbing problem, we are given a set of rectangles in two-dimensional space, with the objective of stabbing all rectangles with the minimum number of lines parallel to the x and y axes. We provide a 2-approximation algorithm, whil...
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ژورنال
عنوان ژورنال: SIAM Journal on Discrete Mathematics
سال: 2006
ISSN: 0895-4801,1095-7146
DOI: 10.1137/s089548010444273x