Approximation Algorithms for Shortest Descending Paths in Terrains

TL;DR

This paper introduces two simple and robust approximation algorithms that efficiently find near-shortest descending paths on polyhedral terrains, a problem previously lacking efficient solutions.

Contribution

The paper presents the first fully polynomial-time approximation schemes (FPTAS) for shortest descending paths on general terrains, improving computational approaches in terrain analysis.

Findings

Two FPTAS algorithms for SDP problem

Algorithms are simple and easy to implement

Achieve near-optimal solutions efficiently

Abstract

A path from s to t on a polyhedral terrain is descending if the height of a point p never increases while we move p along the path from s to t. No efficient algorithm is known to find a shortest descending path (SDP) from s to t in a polyhedral terrain. We give two approximation algorithms (more precisely, FPTASs) that solve the SDP problem on general terrains. Both algorithms are simple, robust and easy to implement.