# An Experimental Study of Algorithms for Geodesic Shortest Paths in the Constant-Workspace Model

## TL;DR

This paper experimentally evaluates algorithms for geodesic shortest paths in simple polygons within the constant-workspace model, comparing three algorithms to the classic Lee-Preparata method, and discusses practical performance and implementation details.

## Contribution

It provides an implementation and empirical comparison of constant-workspace algorithms for geodesic shortest paths, clarifying implementation details and assessing practical efficiency.

## Key findings

- All algorithms perform as theoretically predicted.
- Constant factors in running times are large, limiting practical usefulness.
- The classic Lee-Preparata algorithm remains competitive in practice.

## Abstract

We perform an experimental evaluation of algorithms for finding geodesic shortest paths between two points inside a simple polygon in the constant-workspace model. In this model, the input resides in a read-only array that can be accessed at random. In addition, the algorithm may use a constant number of words for reading and for writing. The constant-workspace model has been studied extensively in recent years, and algorithms for geodesic shortest paths have received particular attention. We have implemented three such algorithms in Python, and we compare them to the classic algorithm by Lee and Preparata that uses linear time and linear space. We also clarify a few implementation details that were missing in the original description of the algorithms. Our experiments show that all algorithms perform as advertised in the original works and according to the theoretical guarantees. However, the constant factors in the running times turn out to be rather large for the algorithms to be fully useful in practice.