Time-Space Trade-off Algorithms for Triangulating a Simple Polygon

TL;DR

This paper introduces a randomized space-efficient algorithm for triangulating simple polygons, optimizing the time-space trade-off and significantly improving performance for limited workspace scenarios.

Contribution

It presents the first randomized $s$-workspace algorithm for polygon triangulation with a novel time complexity trade-off.

Findings

Expected running time of $O(n^2/s + n ext{log} n ext{log}^5(n/s))$

Efficient for $s o 0$, especially when $s o n/ ext{log} n$

Operates with $O(s)$ variables, optimizing space usage.

Abstract

An $s$-workspace algorithm is an algorithm that has read-only access to the values of the input, write-only access to the output, and only uses $O(s)$ additional words of space. We present a randomized $s$-workspace algorithm for triangulating a simple polygon $P$ of $n$ vertices that runs in $O(n^2/s+n \log n \log^{5} (n/s))$ expected time using $O(s)$ variables, for any $s \leq n$. In particular, when $s \leq \frac{n}{\log n\log^{5}\log n}$ the algorithm runs in $O(n^2/s)$ expected time.