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Faster Spectral Sparsification in Dynamic Streams [article]

Michael Kapralov and Aida Mousavifar and Cameron Musco and Christopher Musco and Navid Nouri
2019 arXiv   pre-print
., are presented as a dynamic stream of edge updates) over the past few years, starting with the work of Ahn, Guha and McGregor (SODA'12) on graph connectivity via sketching.  ...  In this paper we consider the problem of designing spectral approximations to graphs, or spectral sparsifiers, using a small number of linear measurements, with the additional constraint that the sketches  ...  This motivates the following goal: Design a sketching algorithm for spectral sparsification in dynamic streams that achieves better than n 3/2 space and decoding time simultaneously.  ... 
arXiv:1903.12165v1 fatcat:yxhpopn5ifbzvcedq6o24trzoe

A Framework for Analyzing Resparsification Algorithms [article]

Rasmus Kyng, Jakub Pachocki, Richard Peng, Sushant Sachdeva
2016 arXiv   pre-print
In recent years, there has been interest in computing spectral sparsifiers in semi-streaming and dynamic settings.  ...  This improves on previous best semi-streaming algorithms for both spectral and cut sparsifiers by a factor of n in both space and runtime.  ...  This result is similar to the ones from [CCPP14] , and improves the dynamic sparsification algorithms in [ADK + 16] by a factor of log 2 n.  ... 
arXiv:1611.06940v1 fatcat:nziw3pob55dvlmhdhpqu4pbcsi

Spectral Sparsification in Dynamic Graph Streams [chapter]

Kook Jin Ahn, Sudipto Guha, Andrew McGregor
2013 Lecture Notes in Computer Science  
(SODA 2012, PODS 2012 gives rise to the first data stream algorithm for the construction of spectral sparsifiers in the dynamic setting where edges can be added or removed from the stream.  ...  cut information (in the case of combinatorial sparsifiers) and additional spectral information (in the case of spectral sparsifiers).  ...  Dynamic Graph Streams and Sketches.  ... 
doi:10.1007/978-3-642-40328-6_1 fatcat:agzu7blp3zc45c3dc2qot7mcui

Spectral Sparsification in the Semi-streaming Setting

Jonathan A. Kelner, Alex Levin
2012 Theory of Computing Systems  
The strongest commonly-used notion of sparsification is spectral sparsification; H is a spectral sparsifier of G if the quadratic forms induced by the Laplacians of G and H approximate one another well  ...  In this paper, we consider a semi-streaming setting, where we have onlyÕ(n) storage space, and we thus cannot keep all of G.  ...  Recently, Spielman and Teng [10] defined the notion of spectral sparsification.  ... 
doi:10.1007/s00224-012-9396-1 fatcat:g2pmivg6gfhzjgiej7yf62k4da

Graph stream algorithms

Andrew McGregor
2014 SIGMOD record  
Over the last decade, there has been considerable interest in designing algorithms for processing massive graphs in the data stream model.  ...  The original motivation was two-fold: a) in many applications, the dynamic graphs that arise are too large to be stored in the main memory of a single machine and b) considering graph problems yields new  ...  Min-Cut and Sparsification In this section we revisit graph sparsification in the context of dynamic graphs.  ... 
doi:10.1145/2627692.2627694 fatcat:r4jv5erzozel7epluhnduywjze

Dynamic Streaming Spectral Sparsification in Nearly Linear Time and Space [article]

Michael Kapralov and Navid Nouri and Aaron Sidford and Jakab Tardos
2019 arXiv   pre-print
In this paper we consider the problem of computing spectral approximations to graphs in the single pass dynamic streaming model.  ...  recovers a spectral sparsifier in Õ(n) time.  ...  Theorem 1 (Near Optimal Streaming Spectral Sparsification).  ... 
arXiv:1903.12150v1 fatcat:55r4ia2nuzdbvjiwhaudzz4xse

An Optimal Lower Bound for Monotonicity Testing over Hypergrids [chapter]

Deeparnab Chakrabarty, C. Seshadhri
2013 Lecture Notes in Computer Science  
Sparsification in Dynamic Graph Streams Kook Jin Ahn, Sudipto Guha and Andrew McGregor Generalizing the Layering Method of Indyk and Woodruff: Recursive Sketches for Frequency-Based Vectors on Streams  ...  Forbes and Amir Shpilka Pseudorandomness for Regular Branching Programs via Fourier Analysis Omer Reingold, Thomas Steinke and Salil Vadhan 4:36-4:55 Break 4:55-5:40 APPROX A New Regularity Lemma and Faster  ... 
doi:10.1007/978-3-642-40328-6_30 fatcat:tdimjhbxkveu5l724kwo37lina

On Fully Dynamic Graph Sparsifiers

Ittai Abraham, David Durfee, Ioannis Koutis, Sebastian Krinninger, Richard Peng
2016 2016 IEEE 57th Annual Symposium on Foundations of Computer Science (FOCS)  
First, we give a fully dynamic algorithm for maintaining a (1 ±ϵ) -spectral sparsifier with amortized update time poly(n, ϵ^-1).  ...  We initiate the study of dynamic algorithms for graph sparsification problems and obtain fully dynamic algorithms, allowing both edge insertions and edge deletions, that take polylogarithmic time after  ...  Thus, the full dynamic update process of all data structures takes O(poly(log n, −1 )) time per dynamic update ofG.  ... 
doi:10.1109/focs.2016.44 dblp:conf/focs/AbrahamDKKP16 fatcat:tu35ze66lncbdbg32fjv63az5u

Adversarial Robustness of Streaming Algorithms through Importance Sampling [article]

Vladimir Braverman, Avinatan Hassidim, Yossi Matias, Mariano Schain, Sandeep Silwal, Samson Zhou
2021 arXiv   pre-print
In addition, we show that the well-known merge and reduce paradigm in streaming is adversarially robust.  ...  are very prevalent in the streaming literature but suffer from adversarial attacks.  ...  Acknowledgments Sandeep Silwal was supported in part by a NSF Graduate Research Fellowship Program. Samson Zhou was supported by a Simons Investigator Award of David P. Woodruff.  ... 
arXiv:2106.14952v2 fatcat:6u6p5b2idrgptkj5yb7nhmxlcm

Single- and multi-level network sparsification by algebraic distance

Emmanuel John, Ilya Safro
2016 Journal of Complex Networks  
Network sparsification methods play an important role in modern network analysis when fast estimation of computationally expensive properties (such as the diameter, centrality indices, and paths) is required  ...  We also introduce a multilevel framework for sparsification that can be used to control the sparsification process at various coarse-grained resolutions.  ...  This is particularly useful in dynamic graphs [40] , graph streaming algorithms [1] and collective classification [33] .  ... 
doi:10.1093/comnet/cnw025 fatcat:2og6iqo56fg43hqvxeuu3cvw5i

Augmenting the Algebraic Connectivity of Graphs

Bogdan-Adrian Manghiuc, Pan Peng, He Sun, Peter Sanders, Grzegorz Herman, Fabrizio Grandoni
2020 European Symposium on Algorithms  
. - We present an efficient algorithm for the subgraph sparsification problem, and for a wide range of parameters our algorithm runs in almost-linear time, in contrast to the previously best known algorithm  ...  In this work we present an approximate and efficient algorithm for the (k,γ)-spectral augmentability problem, and our algorithm runs in almost-linear time under a wide regime of parameters.  ...  In addition to several results on several constructions of linear-sized spectral sparsifiers mentioned above, there are many studies on constructing spectral sparsifiers in streaming and dynamic settings  ... 
doi:10.4230/lipics.esa.2020.70 dblp:conf/esa/Manghiuc0S20 fatcat:slq5igemwja3vjrfzxc4rrszci

Single- and Multi-level Network Sparsification by Algebraic Distance [article]

Emmanuel John, Ilya Safro
2016 arXiv   pre-print
Network sparsification methods play an important role in modern network analysis when fast estimation of computationally expensive properties (such as the diameter, centrality indices, and paths) is required  ...  We also introduce a multilevel framework for sparsification that can be used to control the sparsification process at various coarse-grained resolutions.  ...  This is particularly useful in dynamic graphs [40] , graph streaming algorithms [1] and collective classification [33] .  ... 
arXiv:1601.05527v1 fatcat:zyou3ffcrzdeniijse4gmyivia

Multigrid and multilevel preconditioners for computational photography

Dilip Krishnan, Richard Szeliski
2011 ACM Transactions on Graphics  
Four-color smoothing provides faster convergence (lower error) than Jacobi.  ...  The computational cost for the ABF approach is less than half of the AMG variants and the error with respect to the gold solution is lower (zoom in to see the differences).  ...  In the subsequent text, we refer to this sparsification as the "7-point stencil" sparsification, since the Hessian matrix after sparsification is on average 7-banded. Pre-sparsification.  ... 
doi:10.1145/2070781.2024211 fatcat:qccdldsp25erhbsd6mqgtytdnq

Auditory Sketches: Very Sparse Representations of Sounds Are Still Recognizable

Vincent Isnard, Marine Taffou, Isabelle Viaud-Delmon, Clara Suied, Trevor Bruce Penney
2016 PLoS ONE  
Sounds in our environment like voices, animal calls or musical instruments are easily recognized by human listeners.  ...  Understanding the key features underlying this robust sound recognition is an important question in auditory science.  ...  voices could elicit special behavioral advantage for voices; in their case, this advantage was provided by faster reaction times.  ... 
doi:10.1371/journal.pone.0150313 pmid:26950589 pmcid:PMC4780819 fatcat:c7ie4rsmnvf3bm4q7m3tfkowja

Structure-Preserving Sparsification of Social Networks [article]

Gerd Lindner, Christian L. Staudt, Michael Hamann, Henning Meyerhenke, Dorothea Wagner
2015 arXiv   pre-print
In addition, we propose a new sparsification method (Local Degree) which preserves edges leading to local hub nodes.  ...  Sparsification reduces the size of networks while preserving structural and statistical properties of interest. Various sparsifying algorithms have been proposed in different contexts.  ...  To achieve said interactivity, we implemented a client for the Gephi Streaming Plugin in NetworKit. It is designed to stream graph objects from and to Gephi utilizing the JSON format.  ... 
arXiv:1505.00564v1 fatcat:gbjjb6axjreereppmbtkfylluy
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