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Dynamic Light Spanners in Doubling Metrics

Authors Sujoy Bhore , Jonathan Conroy , Arnold Filtser

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Subject Classification

ACM Subject Classification
  • Theory of computation → Computational geometry
  • Theory of computation → Routing and network design problems
Keywords
  • Dynamic data structures
  • spanners
  • light-weight
  • Euclidean metrics
  • doubling metrics

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Abstract

A t-spanner of a point set X in a metric space (𝒳, δ) is a graph G with vertex set P such that, for any pair of points u,v ∈ X, the distance between u and v in G is at most t times δ(u,v). We study the problem of maintaining a spanner for a dynamic point set X - that is, when X undergoes a sequence of insertions and deletions - in a metric space of constant doubling dimension. For any constant ε > 0, we maintain a (1+ε)-spanner of P whose total weight remains within a constant factor of the weight of the minimum spanning tree of X. Each update (insertion or deletion) can be performed in poly(log Φ) time, where Φ denotes the aspect ratio of X. Prior to our work, no efficient dynamic algorithm for maintaining a light-weight spanner was known even for point sets in low-dimensional Euclidean space.

Cite As Get BibTex

Sujoy Bhore, Jonathan Conroy, and Arnold Filtser. Dynamic Light Spanners in Doubling Metrics. In 42nd International Symposium on Computational Geometry (SoCG 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 367, pp. 13:1-13:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.SoCG.2026.13

Author Details

Sujoy Bhore
  • Department of Computer Science & Engineering, Indian Institute of Technology Bombay, India
Jonathan Conroy
  • Department of Computer Science, Dartmouth College, Hanover, NH, USA
Arnold Filtser
  • Department of Computer Science, Bar-Ilan University, Ramat Gan, Israel

Funding

  • Bhore, Sujoy: Work supported in part by ANRF ARG-MATRICS, Grant 002465.
  • Conroy, Jonathan: Supported in part by U.S. National Science Foundation Grant No. CCF-2443017.
  • Filtser, Arnold: This research was supported by the ISRAEL SCIENCE FOUNDATION (grant No. 1042/22).

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