ISAAC 2008: Algorithms and Computation pp 728-739

# Covering a Point Set by Two Disjoint Rectangles

• Hee-Kap Ahn
• Sang Won Bae
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5369)

## Abstract

Given a set S of n points in the plane, the disjoint two-rectangle covering problem is to find a pair of disjoint rectangles such that their union contains S and the area of the larger rectangle is minimized. In this paper we consider two variants of this optimization problem: (1) the rectangles are free to rotate but must remain parallel to each other, and (2) one rectangle is axis-parallel but the other rectangle is allowed to have an arbitrary orientation. For both of the problems, we present O(n2logn)-time algorithms using O(n) space.

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