3 Search Results for "Vorotnikova, Sofya"

Document

DOI: 10.4230/LIPIcs.CCC.2024.7

Polynomial Pass Semi-Streaming Lower Bounds for K-Cores and Degeneracy

Authors: Sepehr Assadi, Prantar Ghosh, Bruno Loff, Parth Mittal, and Sagnik Mukhopadhyay

Published in: LIPIcs, Volume 300, 39th Computational Complexity Conference (CCC 2024)

Abstract

The following question arises naturally in the study of graph streaming algorithms: Is there any graph problem which is "not too hard", in that it can be solved efficiently with total communication (nearly) linear in the number n of vertices, and for which, nonetheless, any streaming algorithm with Õ(n) space (i.e., a semi-streaming algorithm) needs a polynomial n^Ω(1) number of passes? Assadi, Chen, and Khanna [STOC 2019] were the first to prove that this is indeed the case. However, the lower bounds that they obtained are for rather non-standard graph problems. Our first main contribution is to present the first polynomial-pass lower bounds for natural "not too hard" graph problems studied previously in the streaming model: k-cores and degeneracy. We devise a novel communication protocol for both problems with near-linear communication, thus showing that k-cores and degeneracy are natural examples of "not too hard" problems. Indeed, previous work have developed single-pass semi-streaming algorithms for approximating these problems. In contrast, we prove that any semi-streaming algorithm for exactly solving these problems requires (almost) Ω(n^{1/3}) passes. The lower bound follows by a reduction from a generalization of the hidden pointer chasing (HPC) problem of Assadi, Chen, and Khanna, which is also the basis of their earlier semi-streaming lower bounds. Our second main contribution is improved round-communication lower bounds for the underlying communication problems at the basis of these reductions: - We improve the previous lower bound of Assadi, Chen, and Khanna for HPC to achieve optimal bounds for this problem. - We further observe that all current reductions from HPC can also work with a generalized version of this problem that we call MultiHPC, and prove an even stronger and optimal lower bound for this generalization. These two results collectively allow us to improve the resulting pass lower bounds for semi-streaming algorithms by a polynomial factor, namely, from n^{1/5} to n^{1/3} passes.

Cite as

Sepehr Assadi, Prantar Ghosh, Bruno Loff, Parth Mittal, and Sagnik Mukhopadhyay. Polynomial Pass Semi-Streaming Lower Bounds for K-Cores and Degeneracy. In 39th Computational Complexity Conference (CCC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 300, pp. 7:1-7:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{assadi_et_al:LIPIcs.CCC.2024.7,
  author =	{Assadi, Sepehr and Ghosh, Prantar and Loff, Bruno and Mittal, Parth and Mukhopadhyay, Sagnik},
  title =	{{Polynomial Pass Semi-Streaming Lower Bounds for K-Cores and Degeneracy}},
  booktitle =	{39th Computational Complexity Conference (CCC 2024)},
  pages =	{7:1--7:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-331-7},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{300},
  editor =	{Santhanam, Rahul},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2024.7},
  URN =		{urn:nbn:de:0030-drops-204035},
  doi =		{10.4230/LIPIcs.CCC.2024.7},
  annote =	{Keywords: Graph streaming, Lower bounds, Communication complexity, k-Cores and degeneracy}
}

Document

DOI: 10.4230/OASIcs.SOSA.2018.14

A Simple, Space-Efficient, Streaming Algorithm for Matchings in Low Arboricity Graphs

Authors: Andrew McGregor and Sofya Vorotnikova

Published in: OASIcs, Volume 61, 1st Symposium on Simplicity in Algorithms (SOSA 2018)

Abstract

We present a simple single-pass data stream algorithm using O((log n)/eps^2) space that returns an (alpha + 2)(1 + eps) approximation to the size of the maximum matching in a graph of arboricity alpha.

Cite as

Andrew McGregor and Sofya Vorotnikova. A Simple, Space-Efficient, Streaming Algorithm for Matchings in Low Arboricity Graphs. In 1st Symposium on Simplicity in Algorithms (SOSA 2018). Open Access Series in Informatics (OASIcs), Volume 61, pp. 14:1-14:4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{mcgregor_et_al:OASIcs.SOSA.2018.14,
  author =	{McGregor, Andrew and Vorotnikova, Sofya},
  title =	{{A Simple, Space-Efficient, Streaming Algorithm for Matchings in Low Arboricity Graphs}},
  booktitle =	{1st Symposium on Simplicity in Algorithms (SOSA 2018)},
  pages =	{14:1--14:4},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-064-4},
  ISSN =	{2190-6807},
  year =	{2018},
  volume =	{61},
  editor =	{Seidel, Raimund},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.SOSA.2018.14},
  URN =		{urn:nbn:de:0030-drops-82959},
  doi =		{10.4230/OASIcs.SOSA.2018.14},
  annote =	{Keywords: data streams, matching, planar graphs, arboricity}
}

Document

DOI: 10.4230/LIPIcs.APPROX-RANDOM.2016.17

Planar Matching in Streams Revisited

Authors: Andrew McGregor and Sofya Vorotnikova

Published in: LIPIcs, Volume 60, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2016)

Abstract

We present data stream algorithms for estimating the size or weight of the maximum matching in low arboricity graphs. A large body of work has focused on improving the constant approximation factor for general graphs when the data stream algorithm is permitted O(n polylog n) space where n is the number of nodes. This space is necessary if the algorithm must return the matching. Recently, Esfandiari et al. (SODA 2015) showed that it was possible to estimate the maximum cardinality of a matching in a planar graph up to a factor of 24+epsilon using O(epsilon^{-2} n^{2/3} polylog n) space. We first present an algorithm (with a simple analysis) that improves this to a factor 5+epsilon using the same space. We also improve upon the previous results for other graphs with bounded arboricity. We then present a factor 12.5 approximation for matching in planar graphs that can be implemented using O(log n) space in the adjacency list data stream model where the stream is a concatenation of the adjacency lists of the graph. The main idea behind our results is finding "local" fractional matchings, i.e., fractional matchings where the value of any edge e is solely determined by the edges sharing an endpoint with e. Our work also improves upon the results for the dynamic data stream model where the stream consists of a sequence of edges being inserted and deleted from the graph. We also extend our results to weighted graphs, improving over the bounds given by Bury and Schwiegelshohn (ESA 2015), via a reduction to the unweighted problem that increases the approximation by at most a factor of two.

Cite as

Andrew McGregor and Sofya Vorotnikova. Planar Matching in Streams Revisited. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 60, pp. 17:1-17:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{mcgregor_et_al:LIPIcs.APPROX-RANDOM.2016.17,
  author =	{McGregor, Andrew and Vorotnikova, Sofya},
  title =	{{Planar Matching in Streams Revisited}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2016)},
  pages =	{17:1--17:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-018-7},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{60},
  editor =	{Jansen, Klaus and Mathieu, Claire and Rolim, Jos\'{e} D. P. and Umans, Chris},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2016.17},
  URN =		{urn:nbn:de:0030-drops-66407},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2016.17},
  annote =	{Keywords: data streams, planar graphs, arboricity, matchings}
}

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2 McGregor, Andrew
2 Vorotnikova, Sofya
1 Assadi, Sepehr
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1 Theory of computation → Graph algorithms analysis
1 Theory of computation → Lower bounds and information complexity
1 Theory of computation → Streaming, sublinear and near linear time algorithms

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2 arboricity
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