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Shortest Path Map Equivalence Decompositions and Applications

Author Haitao Wang

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LIPIcs.ESA.2026.160.pdf
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  • 20 pages

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ACM Subject Classification
  • Theory of computation → Computational geometry
  • Theory of computation → Design and analysis of algorithms
Keywords
  • shortest paths
  • shortest path maps
  • SPM-equivalent decompositions
  • two-point shortest path queries
  • geodesic diameter
  • geodesic center
  • polygononal domains

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Abstract

Given a polygonal domain 𝒫 in the plane, the shortest path map with respect to a point s, denoted by SPM(s), is the decomposition of 𝒫 into cells such that shortest paths from s to all points t in the same cell have the same vertex sequence. The shortest path map equivalence decomposition of 𝒫 is the decomposition of 𝒫 into cells so that SPM(s) is topologically equivalent for all points s in the same cell. In this paper, we prove new upper bounds on the combinatorial complexities of the SPM-equivalence decompositions under various settings, depending on whether s and/or t are restricted to be the boundary of 𝒫. We also propose new algorithms to compute these decompositions. Further, our results lead to new solutions to several other problems, including answering two-point shortest path queries in 𝒫, and computing geodesic diameter and center of 𝒫.

Cite As Get BibTex

Haitao Wang. Shortest Path Map Equivalence Decompositions and Applications. In 34th Annual European Symposium on Algorithms (ESA 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 388, pp. 160:1-160:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.ESA.2026.160

Author Details

Haitao Wang
  • Kahlert School of Computing, University of Utah, Salt Lake City, UT, USA

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