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Single Pass Spectral Sparsification in Dynamic Streams
[article]
2015
arXiv
pre-print
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We present the first single pass algorithm for computing spectral sparsifiers of graphs in the dynamic semi-streaming model. ...
work, the best known single pass algorithm for maintaining spectral sparsifiers in dynamic streams required sketches of dimension Omega((1/epsilon^2) n^(5/3)) [AGM14]. ...
Acknowledgements We would like to thank Richard Peng for pointing us to the recursive row sampling algorithm contained in [MP12] , which became a critical component of our streaming algorithm. ...
arXiv:1407.1289v3
fatcat:swm5tbcppnglxmurbz7r5q7y6i
Single Pass Spectral Sparsification in Dynamic Streams
2017
SIAM journal on computing (Print)
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We present the first single pass algorithm for computing spectral sparsifiers of graphs in the dynamic semi-streaming model. ...
best known single pass algorithm for maintaining spectral sparsifiers in dynamic streams required sketches of dimension Ω( 1 2 n 5/3 ) [AGM14]. ...
Acknowledgements We would like to thank Richard Peng for pointing us to the recursive row sampling algorithm contained in [MP12] , which became a critical component of our streaming algorithm. ...
doi:10.1137/141002281
fatcat:nehqritumnhtnoh4edudgvzjaq
Single Pass Spectral Sparsification in Dynamic Streams
2014
2014 IEEE 55th Annual Symposium on Foundations of Computer Science
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We present the first single pass algorithm for computing spectral sparsifiers of graphs in the dynamic semi-streaming model. ...
best known single pass algorithm for maintaining spectral sparsifiers in dynamic streams required sketches of dimension Ω( 1 2 n 5/3 ) [AGM14]. ...
Acknowledgements We would like to thank Richard Peng for pointing us to the recursive row sampling algorithm contained in [MP12] , which became a critical component of our streaming algorithm. ...
doi:10.1109/focs.2014.66
dblp:conf/focs/KapralovLMMS14
fatcat:3hbqkrd4lzc2dmxfhh6jefbppi
Spectral Sparsification in Dynamic Graph Streams
[chapter]
2013
Lecture Notes in Computer Science
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(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). ...
This will be performed in a single-pass over a dynamic graph stream using O( −2 n 5/3 polylog n) space. Let S be the set of samples returned. 2. ...
doi:10.1007/978-3-642-40328-6_1
fatcat:agzu7blp3zc45c3dc2qot7mcui
A Framework for Analyzing Resparsification Algorithms
[article]
2016
arXiv
pre-print
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In recent years, there has been interest in computing spectral sparsifiers in semi-streaming and dynamic settings. ...
of G with O(n n) edges in a single pass over G, using only O(n n) space, and O(m ^2 n) total time. ...
Kelner and Levin [KL13] gave a simple single-pass algorithm for constructing a spectral sparsifier. ...
arXiv:1611.06940v1
fatcat:nziw3pob55dvlmhdhpqu4pbcsi
Graph stream algorithms
2014
SIGMOD record
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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 ...
Over the last decade, there has been considerable interest in designing algorithms for processing massive graphs in the data stream model. ...
Min-Cut and Sparsification In this section we revisit graph sparsification in the context of dynamic graphs. ...
doi:10.1145/2627692.2627694
fatcat:r4jv5erzozel7epluhnduywjze
Single pass sparsification in the streaming model with edge deletions
[article]
2012
arXiv
pre-print
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In this paper we give a construction of cut sparsifiers of Benczur and Karger in the dynamic streaming setting in a single pass over the data stream. ...
Previous constructions either required multiple passes or were unable to handle edge deletions. We use Õ(1/^2) time for each stream update and Õ(n/^2) time to construct a sparsifier. ...
The focus of this paper is to provide a single-pass implementation of cut sparsification on dynamic streams in the semi-streaming model. ...
arXiv:1203.4900v1
fatcat:qjjlfeaoonhsjgafpjnhw6aebq
Dynamic Streaming Spectral Sparsification in Nearly Linear Time and Space
[article]
2019
arXiv
pre-print
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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. ...
A sketch is called oblivious if its distribution is independent of the input -such sketches yield efficient single pass dynamic streaming algorithms for sparsification. ...
arXiv:1903.12150v1
fatcat:55r4ia2nuzdbvjiwhaudzz4xse
Communication-Optimal Distributed Dynamic Graph Clustering
2019
PROCEEDINGS OF THE THIRTIETH AAAI CONFERENCE ON ARTIFICIAL INTELLIGENCE AND THE TWENTY-EIGHTH INNOVATIVE APPLICATIONS OF ARTIFICIAL INTELLIGENCE CONFERENCE
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the message passing and the blackboard models. ...
We consider the problem of clustering graph nodes over large-scale dynamic graphs, such as citation networks, images and web networks, when graph updates such as node/edge insertions/deletions are observed ...
Dynamic Graph Streams. ...
doi:10.1609/aaai.v33i01.33015957
fatcat:pvzm4e4mrjefjhcwlvnjg55s74
Communication-Optimal Distributed Dynamic Graph Clustering
[article]
2018
arXiv
pre-print
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the message passing and the blackboard models. ...
We consider the problem of clustering graph nodes over large-scale dynamic graphs, such as citation networks, images and web networks, when graph updates such as node/edge insertions/deletions are observed ...
Dynamic Graph Streams. ...
arXiv:1811.06072v1
fatcat:5w6oqvitjzas5jdlj3hklols5a
Spectral Sparsification in the Semi-streaming Setting
2012
Theory of Computing Systems
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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 ...
only one pass over G. ...
They then, using an ingenious construction and careful analysis, find a way to implement this in a single pass. ...
doi:10.1007/s00224-012-9396-1
fatcat:g2pmivg6gfhzjgiej7yf62k4da
Graph Sparsification via Refinement Sampling
[article]
2010
arXiv
pre-print
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In this paper, we introduce a new technique for graph sparsification, namely refinement sampling, that gives an Õ(m) time semi-streaming algorithm for graph sparsification. ...
Specifically, we show that refinement sampling can be used to design a one-pass streaming algorithm for sparsification that takes O( n) time per edge, uses O(^2 n) space per node, and outputs an -sparsifier ...
Also, REFINE can be implemented using a single pass over the set of edges. A scheme of refinement relations between S l,k is given in Fig. 1 . ...
arXiv:1004.4915v1
fatcat:wn7uc7e2svglbakiozlllcjtsi
Spanners and sparsifiers in dynamic streams
2014
Proceedings of the 2014 ACM symposium on Principles of distributed computing - PODC '14
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In this paper, we concentrate on the problem of constructing linear sketches of graphs that (approximately) preserve the spectral information of the graph in a few passes over the stream. ...
Linear sketching is a popular technique for computing in dynamic streams, where one needs to handle both insertions and deletions of elements. ...
O(N/D)-ADDITIVE SPANNERS INÕ(ND) SPACE IN A SINGLE PASS In this section we give an algorithm for constructing additive spanners in the dynamic stream model. ...
doi:10.1145/2611462.2611497
dblp:conf/podc/KapralovW14
fatcat:blore6f7rvczjo2a6vulb2yznm
On Fully Dynamic Graph Sparsifiers
2016
2016 IEEE 57th Annual Symposium on Foundations of Computer Science (FOCS)
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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
Graph Spanners by Sketching in Dynamic Streams and the Simultaneous Communication Model
[article]
2020
arXiv
pre-print
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then, and has led to near optimal dynamic streaming algorithms for many fundamental problems such as connectivity, cut and spectral sparsifiers and matchings. ...
In particular, no single pass algorithm is known, and the optimal tradeoff between the number of passes, stretch and space complexity is open. ...
We prove the following theorem in Section 4, as a corollary we obtain a positive answer to the question above (as spectral sparsifier can be computed in a single dynamic stream pass [KLM + 14]). ...
arXiv:2007.14204v2
fatcat:afissnbsu5flxftswo7fbwujp4
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