Minimum-Link Shortest Paths for Polygons amidst Rectilinear Obstacles

TL;DR

This paper introduces an efficient algorithm to compute the shortest rectilinear path with the minimum number of turns between two polygons amidst disjoint rectilinear obstacles, optimizing computational complexity.

Contribution

It presents a novel algorithm that computes minimum-link rectilinear shortest paths between polygons in a plane with disjoint obstacles, improving efficiency.

Findings

Algorithm runs in O((N+n) log (N+n)) time

Uses O(N+n) space complexity

Effective for polygons with disjoint bounding boxes

Abstract

Consider two axis-aligned rectilinear simple polygons in the domain consisting of axis-aligned rectilinear obstacles in the plane such that the bounding boxes, one for each obstacle and one for each polygon, are disjoint. We present an algorithm that computes a minimum-link rectilinear shortest path connecting the two polygons in $O((N+n)\log (N+n))$ time using $O(N+n)$ space, where $n$ is the number of vertices in the domain and $N$ is the total number of vertices of the two polygons.