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Efficient Algorithms for the Bottleneck Path Problem in Geometric Graphs

Authors Matthew J. Katz , Rachel Saban , Micha Sharir

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LIPIcs.MFCS.2026.31.pdf
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Subject Classification

ACM Subject Classification
  • Theory of computation → Computational geometry
Keywords
  • Bottleneck path
  • BFS
  • Antennas
  • Terrain
  • Visibility
  • Bichromatic closest pair
  • Bounded hop
  • Reverse shortest paths

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Abstract

We present efficient algorithms for the bottleneck path problem in two geometric settings that arise naturally in applications: directional-antenna graphs in the plane with antenna angles bounded from below by a constant, and visibility graphs whose vertices lie on or above a 1.5-dimensional terrain, both with Euclidean distances as edge weights. We provide near-linear algorithms for the corresponding decision problems, namely, determining whether the subgraph obtained by retaining all edges with weight at most some threshold bn contains a path from s to t. We then use the decision procedures to obtain algorithms for the bottleneck path problem that run in O^*(n^{8/7}) randomized expected time, where n is the input size and the O^*(⋅) notation hides subpolynomial factors.
Within the same performance bounds, we can also solve the bounded-hop version, in which we only consider s-t paths with at most k edges, for a given integer k < n.

Cite As Get BibTex

Matthew J. Katz, Rachel Saban, and Micha Sharir. Efficient Algorithms for the Bottleneck Path Problem in Geometric Graphs. In 51st International Symposium on Mathematical Foundations of Computer Science (MFCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 386, pp. 31:1-31:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.MFCS.2026.31

Author Details

Matthew J. Katz
  • The Stein Faculty of Computer and Information Science, Ben-Gurion University of the Negev, Beer Sheva, Israel
Rachel Saban
  • The Stein Faculty of Computer and Information Science, Ben-Gurion University of the Negev, Beer Sheva, Israel
Micha Sharir
  • School of Computer Science, Tel Aviv University, Israel

Funding

  • Katz, Matthew J.: Partially supported by Israel Science Foundation Grant 495/23.
  • Saban, Rachel: Partially supported by the Lynne and William Frankel Center for Computer Science and by Israel Science Foundation Grant 495/23.
  • Sharir, Micha: Partially supported by Israel Science Foundation Grant 495/23.

References

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