License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.DISC.2020.15
URN: urn:nbn:de:0030-drops-130938
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2020/13093/
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Su, Hsin-Hao ; Vu, Hoa T.

Distributed Dense Subgraph Detection and Low Outdegree Orientation

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Abstract

The densest subgraph problem, introduced in the 80s by Picard and Queyranne [Networks 1982] as well as Goldberg [Tech. Report 1984], is a classic problem in combinatorial optimization with a wide range of applications. The lowest outdegree orientation problem is known to be its dual problem. We study both the problem of finding dense subgraphs and the problem of computing a low outdegree orientation in the distributed settings.
Suppose G = (V,E) is the underlying network as well as the input graph. Let D denote the density of the maximum density subgraph of G. Our main results are as follows.
- Given a value D̃ ≤ D and 0 < ε < 1, we show that a subgraph with density at least (1-ε)D̃ can be identified deterministically in O((log n) / ε) rounds in the LOCAL model. We also present a lower bound showing that our result for the LOCAL model is tight up to an O(log n) factor.
In the CONGEST~ model, we show that such a subgraph can be identified in O((log³ n) / ε³) rounds with high probability. Our techniques also lead to an O(diameter + (log⁴ n)/ε⁴)-round algorithm that yields a 1-ε approximation to the densest subgraph. This improves upon the previous O(diameter /ε ⋅ log n)-round algorithm by Das Sarma et al. [DISC 2012] that only yields a 1/2-ε approximation.
- Given an integer D̃ ≥ D and Ω(1/D̃) < ε < 1/4, we give a deterministic, Õ((log² n) /ε²)-round algorithm in the CONGEST~ model that computes an orientation where the outdegree of every vertex is upper bounded by (1+ε)D̃. Previously, the best deterministic algorithm and randomized algorithm by Harris [FOCS 2019] run in Õ((log⁶ n)/ ε⁴) rounds and Õ((log³ n) /ε³) rounds respectively and only work in the LOCAL model.

BibTeX - Entry

@InProceedings{su_et_al:LIPIcs:2020:13093,
  author =	{Hsin-Hao Su and Hoa T. Vu},
  title =	{{Distributed Dense Subgraph Detection and Low Outdegree Orientation}},
  booktitle =	{34th International Symposium on Distributed Computing (DISC 2020)},
  pages =	{15:1--15:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-168-9},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{179},
  editor =	{Hagit Attiya},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/13093},
  URN =		{urn:nbn:de:0030-drops-130938},
  doi =		{10.4230/LIPIcs.DISC.2020.15},
  annote =	{Keywords: Distributed Algorithms, Network Algorithms}
}

Keywords: Distributed Algorithms, Network Algorithms
Collection: 34th International Symposium on Distributed Computing (DISC 2020)
Issue Date: 2020
Date of publication: 07.10.2020

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