An Improved Algorithm for Shortest Paths in Weighted Unit-Disk Graphs

Authors

  • Bruce W. Brewer University of Utah
  • Haitao Wang University of Utah

DOI:

https://doi.org/10.57717/cgt.v5i2.69

Abstract

Let V be a set of n points in the plane. The unit-disk graph G = (V, E) has vertex set V and an edge e_uv in E between vertices u, v in V if the Euclidean distance between u and v is at most 1. The weight of each edge e_uv is the Euclidean distance between u and v. Given V and a source point s in V we consider the problem of computing shortest paths in G from s to all other vertices. The previously best algorithm for this problem runs in O(n log2 n) time [Wang and Xue, SoCG'19]. The problem has an Omega(n log n) lower bound under the algebraic decision tree model. In this paper, we present an improved algorithm of O(n log2 n / log log n) time (under the standard real-RAM model). Furthermore, we show that the problem can be solved using O(n log n) comparisons under the algebraic decision tree model, matching the Omega(n log n) lower bound.

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Published

2026-02-04

How to Cite

Brewer, B., & Wang, H. (2026). An Improved Algorithm for Shortest Paths in Weighted Unit-Disk Graphs. Computing in Geometry and Topology, 5(2), 2:1–2:14. https://doi.org/10.57717/cgt.v5i2.69

Issue

Vol. 5 No. 2 (2026)

Section

Original Research Articles

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Copyright (c) 2026 Bruce W. Brewer, Haitao Wang

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