Efficient algorithms for the largest rectangle problem

doi:10.1016/0020-0255(92)90115-O

Information Sciences

Volume 64, Issues 1–2, 1 October 1992, Pages 121-141

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Abstract

In this paper, we present some efficient algorithms for the largest rectangle problem. The problems considered are the following. Problem P1: Given a bounding isothetic rectangle R and a point set S inside it, we have to find out the largest area (perimeter) isothetic rectangle inside R such that it does not contain any point from the set S. Problem P2: Given an isothetic polygon R, we have to find out the largest area (perimeter) rectangle completely contained in R. Problem P3: Same as problem P2, but isothetic holes are allowed inside the polygon R. We present algorithms that run in O(nlogn + K) time for all three problems. Where n is the cardinality of the set S in problem P1 and the number of sides of the polygon R and holes in problems P2 and P3. K is the number of candidate rectangles for a problem instance. The value of K is O(nlogn) on an average. So, our algorithms run in O(nlogn) time in the expected case. But the worst-case running time is O(n²). We also present optimal O(n) time systolic algorithms for all three problems. For problem P1, we present an efficient O(nlogn) time algorithm on a tree of processors.

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View full text

Efficient algorithms for the largest rectangle problem

Abstract

Discrete Appl. Math.

J. Algorithms

Fast algorithms for computing the largest empty rectangle

Geometric applications of a matrix-searching algorithm

Algorithmica

An efficient algorithm for maxdominance, with applications

Algorithmica