Elsevier

Discrete Applied Mathematics

Volume 155, Issue 4, 15 February 2007, Pages 523-537
Discrete Applied Mathematics

An approximation algorithm for dissecting a rectangle into rectangles with specified areas

https://doi.org/10.1016/j.dam.2006.08.005Get rights and content
Under an Elsevier user license
open archive

Abstract

Given a rectangle R with area α and a set of n positive reals A={a1,a2,,an} with aiAai=α, we consider the problem of dissecting R into n rectangles ri with area ai(i=1,2,,n) so that the set R of resulting rectangles minimizes an objective function such as the sum of the perimeters of the rectangles in R, the maximum perimeter of the rectangles in R, and the maximum aspect ratio of the rectangles in R, where we call the problems with these objective functions PERI-SUM, PERI-MAX and ASPECT-RATIO, respectively. We propose an O(nlogn) time algorithm that finds a dissection R of R that is a 1.25-approximate solution to PERI-SUM, a 23-approximate solution to PERI-MAX, and has an aspect ratio at most max{ρ(R),3,1+maxi=1,,n-1ai+1ai}, where ρ(R) denotes the aspect ratio of R.

Keywords

Approximation algorithm
Aspect ratio
Dissection
Divide-and-conquer
Floor plan
Facility layout
NP-hard
Rectangle

Cited by (0)

An extended abstract appeared in the 14th Annual International Symposium on Algorithms and Computation (ISAAC2003) Kyoto, December 15–17.