Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
153 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
45 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

A Time-space Trade-off for Computing the Geodesic Center of a Simple Polygon (1908.11260v1)

Published 29 Aug 2019 in cs.CG

Abstract: In this paper we study the problem of computing the geodesic center of a simple polygon when the available workspace is limited. For an $n$-vertex simple polygon, we give a time-space trade-off algorithm that finds the geodesic center in $O(T(n, s) \log2 n+ \frac{n2}{s} \log n)$ expected time and uses $O(s)$ additional words of space where $s\in \Omega(\log n) \cap O(n)$, and $T(n, s)$ is the time needed for constructing the shortest path tree of a given point inside a simple polygon, in depth-first order, with $O(s)$ extra space. Applying the best current known time-space trade-off of Oh and Ahn (Algorithmica 2019) for shortest path tree, our algorithm runs in $O(\frac{n2}{s} \log3 n)$ expected time.

Summary

We haven't generated a summary for this paper yet.