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A New Balanced Subdivision of a Simple Polygon for Time-Space Trade-Off Algorithms

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Abstract

Given a read-only memory for input and a write-only stream for output, an s-workspace algorithm, for a positive integer parameter s, is an algorithm using only O(s) words of workspace in addition to the memory for the input. In this paper, we present an \(O(n^2/s)\)-time s-workspace algorithm for subdividing a simple n-gon 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 by adopting the proposed subdivision: (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 problem (2) further by applying different approaches depending on the size of the workspace.

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Notes

  1. We say we encounter an extension during the traversal of \(\partial P\) if we reach a foot point or the defining vertex of the extension.

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Authors and Affiliations

  1. Max Planck Institute for Informatics, Saarbrücken, Germany

    Eunjin Oh

  2. Department of Computer Science and Engineering, POSTECH, Pohang, Korea

    Hee-Kap Ahn

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  1. Eunjin Oh
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  2. Hee-Kap Ahn
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Correspondence to Hee-Kap Ahn.

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This research was supported by the MSIT (Ministry of Science and ICT), Korea, under the SW Starlab support program (IITP-2017-0-00905) supervised by the IITP (Institute for Information & Communications Technology Promotion).

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Oh, E., Ahn, HK. A New Balanced Subdivision of a Simple Polygon for Time-Space Trade-Off Algorithms. Algorithmica 81, 2829–2856 (2019). https://doi.org/10.1007/s00453-019-00558-9

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