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Documents authored by Cambus, Mélanie

Document
DOI: 10.4230/LIPIcs.DISC.2023.11
Time and Space Optimal Massively Parallel Algorithm for the 2-Ruling Set Problem

Authors: Mélanie Cambus, Fabian Kuhn, Shreyas Pai, and Jara Uitto

Published in: LIPIcs, Volume 281, 37th International Symposium on Distributed Computing (DISC 2023)

Abstract
In this work, we present a constant-round algorithm for the 2-ruling set problem in the Congested Clique model. As a direct consequence, we obtain a constant round algorithm in the MPC model with linear space-per-machine and optimal total space. Our results improve on the O(log log log n)-round algorithm by [HPS, DISC'14] and the O(log log Δ)-round algorithm by [GGKMR, PODC'18]. Our techniques can also be applied to the semi-streaming model to obtain an O(1)-pass algorithm. Our main technical contribution is a novel sampling procedure that returns a small subgraph such that almost all nodes in the input graph are adjacent to the sampled subgraph. An MIS on the sampled subgraph provides a 2-ruling set for a large fraction of the input graph. As a technical challenge, we must handle the remaining part of the graph, which might still be relatively large. We overcome this challenge by showing useful structural properties of the remaining graph and show that running our process twice yields a 2-ruling set of the original input graph with high probability.
Cite as

Mélanie Cambus, Fabian Kuhn, Shreyas Pai, and Jara Uitto. Time and Space Optimal Massively Parallel Algorithm for the 2-Ruling Set Problem. In 37th International Symposium on Distributed Computing (DISC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 281, pp. 11:1-11:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{cambus_et_al:LIPIcs.DISC.2023.11,
  author =	{Cambus, M\'{e}lanie and Kuhn, Fabian and Pai, Shreyas and Uitto, Jara},
  title =	{{Time and Space Optimal Massively Parallel Algorithm for the 2-Ruling Set Problem}},
  booktitle =	{37th International Symposium on Distributed Computing (DISC 2023)},
  pages =	{11:1--11:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-301-0},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{281},
  editor =	{Oshman, Rotem},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2023.11},
  URN =		{urn:nbn:de:0030-drops-191378},
  doi =		{10.4230/LIPIcs.DISC.2023.11},
  annote =	{Keywords: Ruling Sets, Parallel Algorithms, Congested Clique, Massively Parallel Computing, Semi-Streaming}
}
Document
DOI: 10.4230/LIPIcs.DISC.2021.15
Massively Parallel Correlation Clustering in Bounded Arboricity Graphs

Authors: Mélanie Cambus, Davin Choo, Havu Miikonen, and Jara Uitto

Published in: LIPIcs, Volume 209, 35th International Symposium on Distributed Computing (DISC 2021)

Abstract
Identifying clusters of similar elements in a set is a common task in data analysis. With the immense growth of data and physical limitations on single processor speed, it is necessary to find efficient parallel algorithms for clustering tasks. In this paper, we study the problem of correlation clustering in bounded arboricity graphs with respect to the Massively Parallel Computation (MPC) model. More specifically, we are given a complete graph where the edges are either positive or negative, indicating whether pairs of vertices are similar or dissimilar. The task is to partition the vertices into clusters with as few disagreements as possible. That is, we want to minimize the number of positive inter-cluster edges and negative intra-cluster edges. Consider an input graph G on n vertices such that the positive edges induce a λ-arboric graph. Our main result is a 3-approximation (in expectation) algorithm to correlation clustering that runs in 𝒪(log λ ⋅ poly(log log n)) MPC rounds in the strongly sublinear memory regime. This is obtained by combining structural properties of correlation clustering on bounded arboricity graphs with the insights of Fischer and Noever (SODA '18) on randomized greedy MIS and the PIVOT algorithm of Ailon, Charikar, and Newman (STOC '05). Combined with known graph matching algorithms, our structural property also implies an exact algorithm and algorithms with worst case (1+ε)-approximation guarantees in the special case of forests, where λ = 1.
Cite as

Mélanie Cambus, Davin Choo, Havu Miikonen, and Jara Uitto. Massively Parallel Correlation Clustering in Bounded Arboricity Graphs. In 35th International Symposium on Distributed Computing (DISC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 209, pp. 15:1-15:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{cambus_et_al:LIPIcs.DISC.2021.15,
  author =	{Cambus, M\'{e}lanie and Choo, Davin and Miikonen, Havu and Uitto, Jara},
  title =	{{Massively Parallel Correlation Clustering in Bounded Arboricity Graphs}},
  booktitle =	{35th International Symposium on Distributed Computing (DISC 2021)},
  pages =	{15:1--15:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-210-5},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{209},
  editor =	{Gilbert, Seth},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2021.15},
  URN =		{urn:nbn:de:0030-drops-148173},
  doi =		{10.4230/LIPIcs.DISC.2021.15},
  annote =	{Keywords: MPC Algorithm, Correlation Clustering, Bounded Arboricity}
}
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