Algorithms and hardness for diameter in dynamic graphs

Bertie Ancona; Monika Henzinger; Liam Roditty; Virginia Vassilevska Williams; Nicole Wein

doi:10.4230/LIPIcs.ICALP.2019.13

Algorithms and hardness for diameter in dynamic graphs

Bertie Ancona, Monika Henzinger, Liam Roditty, Virginia Vassilevska Williams, Nicole Wein

Department of Computer Science

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

18 Scopus citations

Abstract

The diameter, radius and eccentricities are natural graph parameters. While these problems have been studied extensively, there are no known dynamic algorithms for them beyond the ones that follow from trivial recomputation after each update or from solving dynamic All-Pairs Shortest Paths (APSP), which is very computationally intensive. This is the situation for dynamic approximation algorithms as well, and even if only edge insertions or edge deletions need to be supported. This paper provides a comprehensive study of the dynamic approximation of Diameter, Radius and Eccentricities, providing both conditional lower bounds, and new algorithms whose bounds are optimal under popular hypotheses in fine-grained complexity. Some of the highlights include: Under popular hardness hypotheses, there can be no significantly better fully dynamic approximation algorithms than recomputing the answer after each update, or maintaining full APSP. Nearly optimal partially dynamic (incremental/decremental) algorithms can be achieved via efficient reductions to (incremental/decremental) maintenance of Single-Source Shortest Paths. For instance, a nearly (3/2+ε)-approximation to Diameter in directed or undirected n-vertex, medge graphs can be maintained decrementally in total time m¹⁺o^(1)√n/ε². This nearly matches the static 3/2-approximation algorithm for the problem that is known to be conditionally optimal.

Original language	English
Title of host publication	46th International Colloquium on Automata, Languages, and Programming, ICALP 2019
Editors	Christel Baier, Ioannis Chatzigiannakis, Paola Flocchini, Stefano Leonardi
Publisher	Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)	9783959771092
DOIs	https://doi.org/10.4230/LIPIcs.ICALP.2019.13
State	Published - 1 Jul 2019
Event	46th International Colloquium on Automata, Languages, and Programming, ICALP 2019 - Patras, Greece Duration: 9 Jul 2019 → 12 Jul 2019

Publication series

Name	Leibniz International Proceedings in Informatics, LIPIcs
Volume	132
ISSN (Print)	1868-8969

Conference

Conference	46th International Colloquium on Automata, Languages, and Programming, ICALP 2019
Country/Territory	Greece
City	Patras
Period	9/07/19 → 12/07/19

Bibliographical note

Publisher Copyright:
© Bertie Ancona, Monika Henzinger, Liam Roditty, Virginia Vassilevska Williams, and Nicole Wein; licensed under Creative Commons License CC-BY

Funding

Funding Monika Henzinger: The research leading to these results has received funding from the European Research Council under the European Community’s Seventh Framework Programme (FP7/2007-2013) / ERC grant agreement No. 340506. Virginia Vassilevska Williams: Supported by an NSF CAREER Award, NSF Grants CCF-1417238, CCF-1528078 and CCF-1514339, a BSF Grant BSF:2012338 and a Sloan Research Fellowship. Nicole Wein: Supported by an NSF Graduate Fellowship and NSF Grant CCF-1514339. Monika Henzinger: The research leading to these results has received funding from the European Research Council under the European Community's Seventh Framework Programme (FP7/2007-2013) / ERC grant agreement No. 340506. Virginia Vassilevska Williams: Supported by an NSF CAREER Award, NSF Grants CCF-1417238, CCF-1528078 and CCF-1514339, a BSF Grant BSF:2012338 and a Sloan Research Fellowship. Nicole Wein: Supported by an NSF Graduate Fellowship and NSF Grant CCF-1514339.

Funders	Funder number
National Science Foundation	CCF-1514339, 340506, 1417238, 1528078, CCF-1528078, BSF:2012338, 1514339, CCF-1417238
Age Endeavour Fellowship
Seventh Framework Programme	FP7/2007-2013
Engineering Research Centers
British Skin Foundation
European Commission

Keywords

Dynamic algorithms
Fine-grained complexity
Graph algorithms

Access to Document

10.4230/LIPIcs.ICALP.2019.13

Cite this

Ancona, B., Henzinger, M., Roditty, L., Williams, V. V., & Wein, N. (2019). Algorithms and hardness for diameter in dynamic graphs. In C. Baier, I. Chatzigiannakis, P. Flocchini, & S. Leonardi (Eds.), 46th International Colloquium on Automata, Languages, and Programming, ICALP 2019 Article 13 (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 132). Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. https://doi.org/10.4230/LIPIcs.ICALP.2019.13

Ancona, Bertie ; Henzinger, Monika ; Roditty, Liam et al. / Algorithms and hardness for diameter in dynamic graphs. 46th International Colloquium on Automata, Languages, and Programming, ICALP 2019. editor / Christel Baier ; Ioannis Chatzigiannakis ; Paola Flocchini ; Stefano Leonardi. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 2019. (Leibniz International Proceedings in Informatics, LIPIcs).

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Ancona, B, Henzinger, M, Roditty, L, Williams, VV & Wein, N 2019, Algorithms and hardness for diameter in dynamic graphs. in C Baier, I Chatzigiannakis, P Flocchini & S Leonardi (eds), 46th International Colloquium on Automata, Languages, and Programming, ICALP 2019., 13, Leibniz International Proceedings in Informatics, LIPIcs, vol. 132, Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 46th International Colloquium on Automata, Languages, and Programming, ICALP 2019, Patras, Greece, 9/07/19. https://doi.org/10.4230/LIPIcs.ICALP.2019.13

Algorithms and hardness for diameter in dynamic graphs. / Ancona, Bertie; Henzinger, Monika; Roditty, Liam et al.
46th International Colloquium on Automata, Languages, and Programming, ICALP 2019. ed. / Christel Baier; Ioannis Chatzigiannakis; Paola Flocchini; Stefano Leonardi. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 2019. 13 (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 132).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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Ancona B, Henzinger M, Roditty L, Williams VV, Wein N. Algorithms and hardness for diameter in dynamic graphs. In Baier C, Chatzigiannakis I, Flocchini P, Leonardi S, editors, 46th International Colloquium on Automata, Languages, and Programming, ICALP 2019. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. 2019. 13. (Leibniz International Proceedings in Informatics, LIPIcs). doi: 10.4230/LIPIcs.ICALP.2019.13

Algorithms and hardness for diameter in dynamic graphs

Abstract

Publication series

Conference

Bibliographical note

Funding

Keywords

Access to Document

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