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

Authors Eunjin Oh, Hee-Kap Ahn



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Eunjin Oh
Hee-Kap Ahn

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Eunjin Oh and Hee-Kap Ahn. A New Balanced Subdivision of a Simple Polygon for Time-Space Trade-off Algorithms. In 28th International Symposium on Algorithms and Computation (ISAAC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 92, pp. 61:1-61:12, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2017)
https://doi.org/10.4230/LIPIcs.ISAAC.2017.61

Abstract

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.
Keywords
  • Time-space trade-off
  • simple polygon
  • shortest path
  • shortest path tree

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References

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