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Related Experiment Video

Updated: Jun 9, 2026

Tree Core Analysis with X-ray Computed Tomography
06:56

Tree Core Analysis with X-ray Computed Tomography

Published on: September 22, 2023

Tree-Packing Revisited: Faster Fully Dynamic Min-Cut and Arboricity.

Tijn de Vos1, Aleksander Christiansen2

  • 1TU Graz, Graz, Austria.

Algorithmica
|June 8, 2026
PubMed
Summary
This summary is machine-generated.

This study introduces improved dynamic algorithms for graph problems by reexamining tree-packings. Faster updates for dynamic min-cut and fractional arboricity are achieved through structural insights into greedy tree-packing.

Keywords:
ArboricityDynamic Graph AlgorithmsMinimum CutTree-Packing

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Area of Science:

  • Graph Theory
  • Algorithms
  • Computer Science

Background:

  • Tree-packings, collections of spanning trees, are crucial for minimum cut and graph parameter studies.
  • Existing dynamic algorithms for min-cut and arboricity rely on tree-packing structures.
  • Previous dynamic min-cut algorithms achieved update times like O~(λ^14.5√n).

Purpose of the Study:

  • To investigate the structural properties of tree-packings and their connection to min-cut and arboricity.
  • To develop faster dynamic algorithms for exact min-cut and fractional arboricity maintenance.
  • To establish new lower bounds for greedy tree-packing.

Main Methods:

  • Analyzing the relationship between tree-packings and graph cuts.
  • Developing a deterministic algorithm for fully dynamic exact min-cut.
  • Designing a deterministic algorithm for maintaining (1+ε)-approximations of fractional arboricity.

Main Results:

  • A deterministic algorithm for fully dynamic exact min-cut with O~(λ^5.5√n) worst-case update time.
  • An improved amortized update time of O~(m^(1-1/12)) for dynamic exact min-cut.
  • The first fully dynamic algorithm for (1+ε)-approximate fractional arboricity with O(α log^6 m / ε^4) amortized update time.

Conclusions:

  • The study provides significant improvements in dynamic graph algorithms through novel structural insights into tree-packings.
  • The new algorithms offer faster update times for fundamental graph problems on multi-graphs.
  • This work advances the understanding of tree-packing structures and their algorithmic applications.