Approximation algorithms for rectangle stabbing and interval stabbing problems

S. Kovaleva, F.C.R. Spieksma

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18 Citations (Scopus)

Abstract

In the weighted rectangle stabbing problem we are given a grid in $\mathbb{R}^2$ 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 being that each rectangle is intersected by at least one column or row. The objective is to find a minimum‐weight (multi)set of columns and rows of the grid so that for each rectangle the total multiplicity of selected columns and rows stabbing it is at least its demand. A special case of this problem, called the interval stabbing problem, arises when each rectangle is intersected by exactly one row. We describe an algorithm called STAB, which is shown to be a constant‐factor approximation algorithm for different variants of this stabbing problem.
Original languageEnglish
Pages (from-to)748-768
JournalSIAM Journal on Discrete Mathematics
Volume20
Issue number3
DOIs
Publication statusPublished - 2006
Externally publishedYes

Keywords

  • rectangle stabbing
  • approximation algorithms
  • combinatorial optimization

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