2026-08-11T08:34:34Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:8240 2024-03-06T10:41:53Z ddc:004 open_access

A New Balanced Subdivision of a Simple Polygon for Time-Space Trade-off Algorithms Oh, Eunjin Ahn, Hee-Kap Time-space trade-off simple polygon shortest path shortest path tree We are given a read-only memory for input and a write-only stream for output. For a positive integer parameter s, an s-workspace algorithm is an algorithm using only O(s) words of workspace in addition to the memory for input. In this paper, we present an O(n^2/s)-time s-workspace algorithm for subdividing a simple polygon into O(\min\{n/s,s\}) subpolygons of complexity O(\max\{n/s,s\}). As applications of the subdivision, the previously best known time-space trade-offs for the following three geometric problems are improved immediately: (1) computing the shortest path between two points inside a simple n-gon, (2) computing the shortest path tree from a point inside a simple n-gon, (3) computing a triangulation of a simple n-gon. In addition, we improve the algorithm for the second problem even further. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Eunjin Oh and Hee-Kap Ahn 2017 Is Part Of LIPIcs, Volume 92, 28th International Symposium on Algorithms and Computation (ISAAC 2017) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ISAAC.2017.61 urn:nbn:de:0030-drops-82401 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2017.61 eng https://creativecommons.org/licenses/by/3.0/legalcode