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Algorithmica

, Volume 81, Issue 1, pp 289–316 | Cite as

An Optimal Algorithm for Minimum-Link Rectilinear Paths in Triangulated Rectilinear Domains

  • Joseph S. B. Mitchell
  • Valentin Polishchuk
  • Mikko Sysikaski
  • Haitao WangEmail author
Article

Abstract

We present a new algorithm for finding minimum-link rectilinear paths among rectilinear obstacles in the plane. Given a triangulated rectilinear domain of h pairwise-disjoint rectilinear obstacles with a total of n vertices, our algorithm can find a minimum-link rectilinear path between any two points in \(O(n+ h \log h)\) time. Further, within the same time our algorithm can build an O(n)-size data structure for any source point s, such that given any query point t, the number of edges of a minimum-link rectilinear path from s to t can be computed in \(O(\log n)\) time and the actual path can be output in additional time linear in the number of the edges of the path. The previously best algorithms for the problems run in \(O(n \log n)\) time.

Notes

Acknowledgements

The authors wish to thank the anonymous reviewers for their suggestions that help improve the presentation of the paper. J. Mitchell acknowledges support from the US-Israel Binational Science Foundation (Grant 2010074) and the National Science Foundation (CCF-1018388, CCF-1526406). H. Wang was supported in part by NSF under Grant CCF-1317143.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Stony Brook UniversityStony BrookUSA
  2. 2.Linköping UniversityLinköpingSweden
  3. 3.GoogleZurichSwitzerland
  4. 4.Utah State UniversityLoganUSA

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