Approximate Shortest Path through a Weighted Planar Subdivision

TL;DR

This paper introduces a polynomial-time approximation algorithm for efficiently computing near-optimal shortest paths in weighted planar subdivisions, where each face has an associated traversal cost.

Contribution

It develops a novel wavefront propagation algorithm that approximates shortest paths in weighted planar subdivisions with provable accuracy.

Findings

Algorithm computes $ ext{epsilon}$-approximate shortest paths efficiently.

Polynomial time complexity of the proposed approximation method.

Applicable to weighted planar subdivisions with arbitrary face weights.

Abstract

This paper presents an approximation algorithm for finding a shortest path between two points $s$ and $t$ in a weighted planar subdivision $\PS$. Each face $f$ of $\PS$ is associated with a weight $w_f$, and the cost of travel along a line segment on $f$ is $w_f$ multiplied by the Euclidean norm of that line segment. The cost of a path which traverses across several faces of the subdivision is the sum of the costs of travel along each face. Our algorithm progreeses the discretized shortest path wavefront from source $s$, and takes polynomial time in finding an $\epsilon$-approximate shortest path.