Linear Time Algorithm for Optimal Feed-link Placement

TL;DR

This paper presents a linear time algorithm for optimally placing a feed-link in a transportation network polygon to minimize the maximum dilation, significantly improving efficiency over previous methods.

Contribution

The authors introduce a novel linear time algorithm for optimal feed-link placement, reducing complexity from roughly O(n log n) to O(n).

Findings

The algorithm computes the optimal feed-link in linear time.

It minimizes the maximum dilation for the extended network.

Performance surpasses previous algorithms in efficiency.

Abstract

Given a polygon representing a transportation network together with a point p in its interior, we aim to extend the network by inserting a line segment, called a feed-link, which connects p to the boundary of the polygon. Once a feed link is fixed, the geometric dilation of some point q on the boundary is the ratio between the length of the shortest path from p to q through the extended network, and their Euclidean distance. The utility of a feed-link is inversely proportional to the maximal dilation over all boundary points. We give a linear time algorithm for computing the feed-link with the minimum overall dilation, thus improving upon the previously known algorithm of complexity that is roughly O(n log n).