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September 28, 2025Open Access

Algorithms for Distance Problems in Continuous Graphs

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The study develops subquadratic time algorithms for diameter and mean distance in continuous graphs, emphasizing sparse graphs.

Computing the diameter and mean distance in continuous graphs is optimized using geometric techniques.
For continuous graphs of treewidth at most k, the algorithms run in O(n log^{O(k)} n) time for n vertices.
Algorithms for continuous planar graphs with n vertices are efficient, taking O(n F log n) time.
Traditional approaches require O(m^2) time, revealing significant improvements with new methods.

Cabello et al. (2025) studied this question.

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September 28, 2025Open Access

View Full Paper

Ask AI

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Authors

The study develops subquadratic time algorithms for diameter and mean distance in continuous graphs, emphasizing sparse graphs.

Computing the diameter and mean distance in continuous graphs is optimized using geometric techniques.
For continuous graphs of treewidth at most k, the algorithms run in O(n log^{O(k)} n) time for n vertices.
Algorithms for continuous planar graphs with n vertices are efficient, taking O(n F log n) time.
Traditional approaches require O(m^2) time, revealing significant improvements with new methods.

Cabello et al. (2025) studied this question.

View Full Paper

Ask AI

Bookmark