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A Simple Proof of a New Set Disjointness with Applications to Data Streams [article]

Akshay Kamath, Eric Price, David P. Woodruff
2021 arXiv   pre-print
We observe for most applications, it instead suffices to look at what we call the "mostly" set disjointness problem, which changes case (2) to say there is a unique element j occurring in at least half  ...  The multiplayer promise set disjointness is one of the most widely used problems from communication complexity in applications.  ...  Acknowledgments The authors would like to thank the anonymous reviewers of a previous version of this paper for helpful suggestions that significantly improved the presentation. D.  ... 
arXiv:2105.11338v1 fatcat:et7royjvsnb25i53ppes5u2pvy

A Simple Proof of a New Set Disjointness with Applications to Data Streams

Akshay Kamath, Eric Price, David P. Woodruff, Valentine Kabanets
2021
We observe for most applications, it instead suffices to look at what we call the "mostly" set disjointness problem, which changes case (2) to say there is a unique element j occurring in at least half  ...  The multiplayer promise set disjointness is one of the most widely used problems from communication complexity in applications.  ...  Acknowledgements The authors would like to thank the anonymous reviewers of a previous version of this paper for helpful suggestions that significantly improved the presentation.  ... 
doi:10.4230/lipics.ccc.2021.37 fatcat:obyp6hjkt5burkqtqnamkintva

Lower Bounds for Multi-Pass Processing of Multiple Data Streams

Nicole Schweikardt, Marc Herbstritt
2009 Symposium on Theoretical Aspects of Computer Science  
This paper gives a brief overview of computation models for data stream processing, and it introduces a new model for multi-pass processing of multiple streams, the so-called mp2s-automata.  ...  The main technical contribution of this paper is the proof of a lower bound on the size of memory and the number of heads that are required for solving the set disjointness problem with mp2s-automata.  ...  I would like to thank Georg Schnitger for helpful comments on an earlier version of this paper.  ... 
doi:10.4230/lipics.stacs.2009.1857 dblp:conf/stacs/Schweikardt09 fatcat:7pithojgefcjtdxpltfu6wrobi

Lower Bounds for Multi-Pass Processing of Multiple Data Streams [article]

Nicole Schweikardt
2009 arXiv   pre-print
This paper gives a brief overview of computation models for data stream processing, and it introduces a new model for multi-pass processing of multiple streams, the so-called mp2s-automata.  ...  The main technical contribution of this paper is the proof of a lower bound on the size of memory and the number of heads that are required for solvin g the set disjointness problem with mp2s-automata.  ...  I would like to thank Georg Schnitger for helpful comments on an earlier version of this paper.  ... 
arXiv:0902.1605v1 fatcat:otgtvhhwxrhgba6d7okb33upqm

The story of set disjointness

Arkadev Chattopadhyay, Toniann Pitassi
2010 ACM SIGACT News  
Acknowledgements We wish to thank the following people for very helpful comments: Scott Aaronson, Joshua Brody, Amit Chakrabarti, Jeff Edmonds, Faith Ellen, Brendan Lucier, Noam Nisan, Michel Schapira,  ...  Here we highlight some applications in the areas of: streaming, data structures, circuit complexity, proof complexity, game theory and quantum computation.  ...  Our first simple application shows that computing F ∞ in the streaming model implies an efficient two-party communication protocol for set disjointness.  ... 
doi:10.1145/1855118.1855133 fatcat:d3zqnoptm5eoxefjpxlaoag44q

Best-Order Streaming Model [chapter]

Atish Das Sarma, Richard J. Lipton, Danupon Nanongkai
2009 Lecture Notes in Computer Science  
This model is closely related to many models of computation in other areas such as data streams, communication complexity, and proof checking, and could be used in applications such as cloud computing.  ...  We study a new model of computation, called best-order stream, for graph problems.  ...  Acknowledgements We would like to thank Justin Thaler and the anonymous reviewers for useful comments.  ... 
doi:10.1007/978-3-642-02017-9_21 fatcat:ppveptqj7jejpadpt2vcohjigm

Best-order streaming model

Atish Das Sarma, Richard J. Lipton, Danupon Nanongkai
2011 Theoretical Computer Science  
This model is closely related to many models of computation in other areas such as data streams, communication complexity, and proof checking, and could be used in applications such as cloud computing.  ...  We study a new model of computation, called best-order stream, for graph problems.  ...  Acknowledgements We would like to thank Justin Thaler and the anonymous reviewers for useful comments.  ... 
doi:10.1016/j.tcs.2010.10.046 fatcat:bmj42j5bdfcoxk4hmdghnm7lze

Join Sizes, Frequency Moments, and Applications [chapter]

Graham Cormode, Minos Garofalakis
2016 Data-Centric Systems and Applications  
space), which is computable in a data stream setting with small space and limited (fourwise) randomness.  ...  For example, suppose the input consists of a set of one-dimensional ranges [a . . . b]. To answer the query of how many intervals contain a given point c, we can simple pose the point query I c .  ... 
doi:10.1007/978-3-540-28608-0_4 fatcat:jw7mwxbmobamrkhvl72brfxk6q

Communication Complexity (for Algorithm Designers)

Tim Roughgarden
2016 Foundations and Trends® in Theoretical Computer Science  
The course begins in Lectures 1-3 with the simple case of one-way communication protocols -where only a single message is sent -and their relevance to algorithm design.  ...  Along the way, we'll also: (3) Get exposure to lots of cool computational models and some famous results about them -data streams and linear sketches, compressive sensing, space-query time trade-offs in  ...  The Data Stream Model The data stream model is motivated by applications in which the input is best thought of as a firehose -packets arriving to a network switch at a torrential rate, or data being generated  ... 
doi:10.1561/0400000076 fatcat:yy7hcyheorerbbbnjq2mkta4ha

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.  ...  We present a new bound relating edge connectivity in a simple, unweighted graph with effective resistance in the corresponding electrical network. The bound is tight.  ...  [1, 12] , and estimating properties of the frequency vectors that arise in data stream applications [7, 13] .  ... 
doi:10.1007/978-3-642-40328-6_1 fatcat:agzu7blp3zc45c3dc2qot7mcui

Kernelization via Sampling with Applications to Finding Matchings and Related Problems in Dynamic Graph Streams

Rajesh Chitnis, Graham Cormode, Hossein Esfandiari, MohammadTaghi Hajiaghayi, Andrew McGregor, Morteza Monemizadeh, Sofya Vorotnikova
2015 Proceedings of the Twenty-Seventh Annual ACM-SIAM Symposium on Discrete Algorithms  
Note that for this application of the subgraph sampling primitive, it suffices to implement the sampling data structure with a counter for each pair of colors: any non-zero count corresponds to an edge  ...  Application to Data Streams and MapReduce We now describe how the subgraph sampling primitive can be implemented in various computational models. Dynamic Graph Streams.  ... 
doi:10.1137/1.9781611974331.ch92 dblp:conf/soda/ChitnisCEHMMV16 fatcat:3jul55k3u5alboeeoughpqk6w4

A Simple Augmentation Method for Matchings with Applications to Streaming Algorithms

Christian Konrad, Michael Wagner
2018 International Symposium on Mathematical Foundations of Computer Science  
The main applications of our method lie in the area of data streaming algorithms, where an algorithm performs few passes over the edges of an n-vertex graph while maintaining a memory of size O(n polylog  ...  To obtain our main result, we combine our method with a residual sparsity property of the random order Greedy algorithm and give a one-pass random order streaming algorithm for MBM with approximation factor  ...  Applications to Data Streaming Algorithms.  ... 
doi:10.4230/lipics.mfcs.2018.74 dblp:conf/mfcs/Konrad18 fatcat:3rpdy46gijaadnk7m7eenqbu2a

Kernelization via Sampling with Applications to Dynamic Graph Streams [article]

Rajesh Chitnis and Graham Cormode and Hossein Esfandiari and MohammadTaghi Hajiaghayi and Andrew McGregor and Morteza Monemizadeh and Sofya Vorotnikova
2015 arXiv   pre-print
In this paper we present a simple but powerful subgraph sampling primitive that is applicable in a variety of computational models including dynamic graph streams (where the input graph is defined by a  ...  Third, there exists an Õ(n^4/5) space algorithm that returns a constant approximation in graphs with bounded arboricity. -- Vertex Cover and Hitting Set: There exists an Õ(k^d) space algorithm that solves  ...  Note that for this application of the subgraph sampling primitive, it suffices to implement the sampling data structure with a counter for each pair of colors: any non-zero count corresponds to an edge  ... 
arXiv:1505.01731v1 fatcat:oh4zxrhluvcydnyynabcjidtgi

Communication Complexity (for Algorithm Designers) [article]

Tim Roughgarden
2015 arXiv   pre-print
Get exposure to lots of cool computational models and some famous results about them --- data streams and linear sketches, compressive sensing, space-query time trade-offs in data structures, sublinear-time  ...  Scratch the surface of techniques for proving communication complexity lower bounds (fooling sets, corruption bounds, etc.).  ...  The Data Stream Model The data stream model is motivated by applications in which the input is best thought of as a firehose -packets arriving to a network switch at a torrential rate, or data being generated  ... 
arXiv:1509.06257v1 fatcat:lgm6hgohzvayfig5bbv4rbzjdi

On graph problems in a semi-streaming model

Joan Feigenbaum, Sampath Kannan, Andrew McGregor, Siddharth Suri, Jian Zhang
2005 Theoretical Computer Science  
We formalize a potentially rich new streaming model, the semi-streaming model, that we believe is necessary for the fruitful study of efficient algorithms for solving problems on massive graphs whose edge  ...  Unless stated otherwise, we denote by G(V, E) a graph G with vertex set V = {v 1 , v 2 , . . . , v n } and edge set E = {e 1 , e 2 , . . . , e m }.  ...  Conclusion We considered a set of classical graph problems in the semi-streaming model.  ... 
doi:10.1016/j.tcs.2005.09.013 fatcat:am5i2stnv5h4bjmazgkzbfohsu
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