Packing Boundary-Anchored Rectangles and Squares

Therese Biedl; Ahmad Biniaz; Anil Maheshwari; Saeed Mehrabi

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arXiv · 1906.11948

Packing Boundary-Anchored Rectangles and Squares

Therese Biedl·Ahmad Biniaz·Anil Maheshwari·Saeed Mehrabi

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Abstract

Consider a set $P$ of $n$ points on the boundary of an axis-aligned square $Q$. We study the boundary-anchored packing problem on $P$ in which the goal is to find a set of interior-disjoint axis-aligned rectangles in $Q$ such that each rectangle is anchored (has a corner at some point in $P$), each point in $P$ is used to anchor at most one rectangle, and the total area of the rectangles is maximized. Here, a rectangle is anchored at a point $p$ in $P$ if one of its corners coincides with $p$. In this paper, we show how to solve this problem in time linear in $n$, provided that the points of $P$ are given in sorted order along the boundary of $Q$. We also consider the problem for anchoring squares and give an $O(n^4)$-time algorithm when the points in $P$ lie on two opposite sides of $Q$.

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BibTeX RIS

Therese Biedl, Ahmad Biniaz, Anil Maheshwari, Saeed Mehrabi. 2019-06-27. Packing Boundary-Anchored Rectangles and Squares. https://arxiv.org/abs/1906.11948

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