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International Computing and Combinatorics Conference

COCOON 2019: Computing and Combinatorics pp 1–12Cite as

Fully Dynamic Arboricity Maintenance

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11653))

Abstract

Given an undirected graph, its arboricity is the minimum number of edge disjoint forests, its edge set can be partitioned into. We develop the first fully dynamic algorithms to determine the arboricity of a graph under edge insertions and deletions. While our insertion algorithm is based on known static algorithms to determine the arboricity, our deletion algorithm is, to the best of our knowledge, new.

Our algorithms take \({\tilde{O}} (m)\) time (\({\tilde{O}}\) notation ignores logarithmic factors.) to insert or delete an edge where m is the number of edges in the graph while the best static algorithm to compute arboricity takes \(O(m^{3/2}\log (n^2/m))\) time [7].

We complement our upper bound with a lower bound result of amortized \(\varOmega (\log n)\) for any algorithm that maintains a forest decomposition of size arboricity of the graph under edge insertions and deletions.

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Notes

  1. 1.

    Proofs of results marked \(\star \) are deferred to the full version.

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Authors and Affiliations

  1. The Institute of Mathematical Sciences, HBNI, CIT Campus, Taramani, Chennai, 600 113, India

    Niranka Banerjee, Venkatesh Raman & Saket Saurabh

Authors
  1. Niranka Banerjee
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  2. Venkatesh Raman
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  3. Saket Saurabh
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Corresponding author

Correspondence to Niranka Banerjee .

Editor information

Editors and Affiliations

  1. The University of Texas at Dallas, Richardson, TX, USA

    Ding-Zhu Du

  2. Xidian University, Xi'an, China

    Zhenhua Duan

  3. Xidian University, Xi'an, China

    Cong Tian

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Banerjee, N., Raman, V., Saurabh, S. (2019). Fully Dynamic Arboricity Maintenance. In: Du, DZ., Duan, Z., Tian, C. (eds) Computing and Combinatorics. COCOON 2019. Lecture Notes in Computer Science(), vol 11653. Springer, Cham. https://doi.org/10.1007/978-3-030-26176-4_1

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  • DOI: https://doi.org/10.1007/978-3-030-26176-4_1

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-26175-7

  • Online ISBN: 978-3-030-26176-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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