Minimum-Width Double-Strip and Parallelogram Annulus

TL;DR

This paper introduces the first algorithms for computing minimum-width double-strip and parallelogram annulus regions that enclose a set of points, with complexities of O(n^2) and O(n^3 log n) respectively, allowing free orientation.

Contribution

It provides the first algorithms for these geometric problems, achieving optimal time complexities for free orientation cases.

Findings

Algorithms for minimum-width double-strip and parallelogram annulus

Time complexities of O(n^2) and O(n^3 log n)

Applicable to arbitrary orientations

Abstract

In this paper, we study the problem of computing a minimum-width double-strip or parallelogram annulus that encloses a given set of $n$ points in the plane. A double-strip is a closed region in the plane whose boundary consists of four parallel lines and a parallelogram annulus is a closed region between two edge-parallel parallelograms. We present several first algorithms for these problems. Among them are $O(n^2)$ and $O(n^3 \log n)$-time algorithms that compute a minimum-width double-strip and parallelogram annulus, respectively, when their orientations can be freely chosen.