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May 29, 20260 citationsOpen Access

Diameter Computation for Intersection Graphs in 3D and Higher Dimensions

Charting the Diameter Computation Landscape of Intersection Graphs in 3D and Above

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Authors

TCTimothy M. ChanHCHsien-Chih ChangJGJie Gao

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Overview

Randomized trial reveals new algorithms for diameter computation in 3D intersection graphs, indicating progress in complexity analysis.

Key Points

  • This research aims to explore and improve the computation of graph diameter in three and higher dimensions, especially for intersection graphs.
  • Developed a subquadratic-time algorithm for determining Diameter-3 of unit cubes in 3D.
  • Established lower bounds for Diameter-3 of unit balls under the Orthogonal Vector hypothesis.
  • Created a near-linear-time algorithm for Diameter-2 of unit cubes in 3D.
  • Presented the first subquadratic-time algorithm for Diameter-3 of unit cubes in 3D.
  • Achieved a truly subquadratic-time lower bound for Diameter-3 of unit balls under the OV hypothesis.
  • Developed a near-linear-time algorithm for Diameter-2 of unit cubes in 3D.

Cite This Study

Chan et al. (2026) studied this question.

synapsesocial.com/papers/6a192dd1fab5b468c4416c37https://doi.org/10.4230/lipics.socg.2026.29
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Also Consider

Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context:

  1. 1The Complexity of Diameter on H-free graphs2024
  2. 2Computing the Polytope Diameter is Even Harder than NP-hard (Already for Perfect Matchings)2025
  3. 3On finite sphere packings and coverings2026
  4. 4Algorithms for Distance Problems in Continuous Graphs2025
  5. 5Diameter reduction via arc reversal2024