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Computing the Exact Radius of Large Graphs

Authors Stefan Funke , Claudius Proissl , Sabine Storandt

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Subject Classification

ACM Subject Classification
  • Theory of computation → Graph algorithms analysis
  • Theory of computation → Parameterized complexity and exact algorithms
Keywords
  • Radius
  • Graph Center
  • LP-type
  • Combinatorial Dimension

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Abstract

The radius of a graph is an important structural parameter which plays a key role in social network analysis and related applications. It measures the minimum shortest path distance that is required to reach all nodes in the graph from a single node. A node from which all other nodes are within a distance equal to the radius is called a center of the graph. In a graph with n nodes and m edges, the center and the radius can be determined in Õ(nm) by computing shortest path distances between all pairs of nodes. Fine-grained complexity results suggest that asymptotically faster algorithms are unlikely to exist. In this paper, we describe a novel randomized algorithm for exact radius computation in weighted digraphs with an expected running time in Õ(d³m) where d is the so-called combinatorial dimension. Our methodology is inspired by Clarkson’s algorithm for LP-type problems. The value of d denotes the size of a basis, which is a smallest subset of nodes which enforce the same radius as the whole node set. While we show that there exist graphs with d ∈ Θ(n), our empirical analysis reveals that even large real-world graphs have small combinatorial dimension. This allows us to compute the radius in near-linear time on such instances. The significantly improved scalability can be clearly observed in our experimental evaluation on a diverse set of benchmark graphs.

Cite As Get BibTex

Stefan Funke, Claudius Proissl, and Sabine Storandt. Computing the Exact Radius of Large Graphs. In 23rd International Symposium on Experimental Algorithms (SEA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 338, pp. 17:1-17:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.SEA.2025.17

Author Details

Stefan Funke
  • Universität Stuttgart, Germany
Claudius Proissl
  • Universität Stuttgart, Germany
Sabine Storandt
  • Universität Konstanz, Germany

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