3 Search Results for "Crouch, Michael"

Document
DOI: 10.4230/LIPIcs.ISAAC.2021.73
Maximum-Weight Matching in Sliding Windows and Beyond

Authors: Leyla Biabani, Mark de Berg, and Morteza Monemizadeh

Published in: LIPIcs, Volume 212, 32nd International Symposium on Algorithms and Computation (ISAAC 2021)

Abstract
We study the maximum-weight matching problem in the sliding-window model. In this model, we are given an adversarially ordered stream of edges of an underlying edge-weighted graph G(V,E), and a parameter L specifying the window size, and we want to maintain an approximation of the maximum-weight matching of the current graph G(t); here G(t) is defined as the subgraph of G consisting of the edges that arrived during the time interval [max(t-L,1),t], where t is the current time. The goal is to do this with Õ(n) space, where n is the number of vertices of G. We present a deterministic (3.5+ε)-approximation algorithm for this problem, thus significantly improving the (6+ε)-approximation algorithm due to Crouch and Stubbs [Michael S. Crouch and Daniel M. Stubbs, 2014]. We also present a generic machinery for approximating subadditve functions in the sliding-window model. A function f is called subadditive if for every disjoint substreams A, B of a stream S it holds that f(AB) ⩽ f(A) + f(B), where AB denotes the concatenation of A and B. We show that given an α-approximation algorithm for a subadditive function f in the insertion-only model we can maintain a (2α+ε)-approximation of f in the sliding-window model. This improves upon recent result Krauthgamer and Reitblat [Robert Krauthgamer and David Reitblat, 2019], who obtained a (2α²+ε)-approximation.
Cite as

Leyla Biabani, Mark de Berg, and Morteza Monemizadeh. Maximum-Weight Matching in Sliding Windows and Beyond. In 32nd International Symposium on Algorithms and Computation (ISAAC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 212, pp. 73:1-73:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{biabani_et_al:LIPIcs.ISAAC.2021.73,
  author =	{Biabani, Leyla and de Berg, Mark and Monemizadeh, Morteza},
  title =	{{Maximum-Weight Matching in Sliding Windows and Beyond}},
  booktitle =	{32nd International Symposium on Algorithms and Computation (ISAAC 2021)},
  pages =	{73:1--73:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-214-3},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{212},
  editor =	{Ahn, Hee-Kap and Sadakane, Kunihiko},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2021.73},
  URN =		{urn:nbn:de:0030-drops-155061},
  doi =		{10.4230/LIPIcs.ISAAC.2021.73},
  annote =	{Keywords: maximum-weight matching, sliding-window model, approximation algorithm, and subadditve functions}
}
Document
DOI: 10.4230/LIPIcs.ESA.2016.32
Stochastic Streams: Sample Complexity vs. Space Complexity

Authors: Michael Crouch, Andrew McGregor, Gregory Valiant, and David P. Woodruff

Published in: LIPIcs, Volume 57, 24th Annual European Symposium on Algorithms (ESA 2016)

Abstract
We address the trade-off between the computational resources needed to process a large data set and the number of samples available from the data set. Specifically, we consider the following abstraction: we receive a potentially infinite stream of IID samples from some unknown distribution D, and are tasked with computing some function f(D). If the stream is observed for time t, how much memory, s, is required to estimate f(D)? We refer to t as the sample complexity and s as the space complexity. The main focus of this paper is investigating the trade-offs between the space and sample complexity. We study these trade-offs for several canonical problems studied in the data stream model: estimating the collision probability, i.e., the second moment of a distribution, deciding if a graph is connected, and approximating the dimension of an unknown subspace. Our results are based on techniques for simulating different classical sampling procedures in this model, emulating random walks given a sequence of IID samples, as well as leveraging a characterization between communication bounded protocols and statistical query algorithms.
Cite as

Michael Crouch, Andrew McGregor, Gregory Valiant, and David P. Woodruff. Stochastic Streams: Sample Complexity vs. Space Complexity. In 24th Annual European Symposium on Algorithms (ESA 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 57, pp. 32:1-32:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{crouch_et_al:LIPIcs.ESA.2016.32,
  author =	{Crouch, Michael and McGregor, Andrew and Valiant, Gregory and Woodruff, David P.},
  title =	{{Stochastic Streams: Sample Complexity vs. Space Complexity}},
  booktitle =	{24th Annual European Symposium on Algorithms (ESA 2016)},
  pages =	{32:1--32:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-015-6},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{57},
  editor =	{Sankowski, Piotr and Zaroliagis, Christos},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2016.32},
  URN =		{urn:nbn:de:0030-drops-63838},
  doi =		{10.4230/LIPIcs.ESA.2016.32},
  annote =	{Keywords: data streams, sample complexity, frequency moments, graph connectivity, subspace approximation}
}
Document
DOI: 10.4230/LIPIcs.APPROX-RANDOM.2014.96
Improved Streaming Algorithms for Weighted Matching, via Unweighted Matching

Authors: Michael Crouch and Daniel M. Stubbs

Published in: LIPIcs, Volume 28, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2014)

Abstract
We present a (4 + epsilon) approximation algorithm for weighted graph matching which applies in the semistreaming, sliding window, and MapReduce models; this single algorithm improves the previous best algorithm in each model. The algorithm operates by reducing the maximum-weight matching problem to a polylog number of copies of the maximum-cardinality matching problem. The algorithm also extends to provide approximation guarantees for the more general problem of finding weighted independent sets in p-systems (which include intersections of p matroids and p-bounded hypergraph matching).
Cite as

Michael Crouch and Daniel M. Stubbs. Improved Streaming Algorithms for Weighted Matching, via Unweighted Matching. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2014). Leibniz International Proceedings in Informatics (LIPIcs), Volume 28, pp. 96-104, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)

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@InProceedings{crouch_et_al:LIPIcs.APPROX-RANDOM.2014.96,
  author =	{Crouch, Michael and Stubbs, Daniel M.},
  title =	{{Improved Streaming Algorithms for Weighted Matching, via Unweighted Matching}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2014)},
  pages =	{96--104},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-74-3},
  ISSN =	{1868-8969},
  year =	{2014},
  volume =	{28},
  editor =	{Jansen, Klaus and Rolim, Jos\'{e} and Devanur, Nikhil R. and Moore, Cristopher},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2014.96},
  URN =		{urn:nbn:de:0030-drops-46907},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2014.96},
  annote =	{Keywords: Streaming Algorithms, Graph Matching, Weighted Graph Matching, MapReduce, Independence Systems}
}
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