Single-Point Visibility Constraint Minimum Link Paths in Simple Polygons

TL;DR

This paper presents an optimal linear-time algorithm for finding a minimum link path within a simple polygon that ensures visibility of a target point from at least one point on the path, addressing a visibility constraint problem.

Contribution

It introduces a novel linear-time algorithm for the visibility-constrained minimum link path problem in simple polygons, improving efficiency over previous methods.

Findings

Achieves $O(n)$ time complexity for the problem.

Provides a method to incorporate visibility constraints into minimum link paths.

Extends the shortest path map (SPM) approach for this specific problem.

Abstract

We address the following problem: Given a simple polygon $P$ with $n$ vertices and two points $s$ and $t$ inside it, find a minimum link path between them such that a given target point $q$ is visible from at least one point on the path. The method is based on partitioning a portion of $P$ into a number of faces of equal link distance from a source point. This partitioning is essentially a shortest path map (SPM). In this paper, we present an optimal algorithm with $O(n)$ time bound, which is the same as the time complexity of the standard minimum link paths problem.