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On the communication and streaming complexity of maximum bipartite matching [chapter]

Ashish Goel, Michael Kapralov, Sanjeev Khanna
2012 Proceedings of the Twenty-Third Annual ACM-SIAM Symposium on Discrete Algorithms  
The focus of this work is to understand one-round communication complexity and one-pass streaming complexity of maximum bipartite matching.  ...  The minimum message length is the one-round communication complexity of approximating bipartite matching.  ...  Introduction We study the communication and streaming complexity of the maximum bipartite matching problem. Consider the following scenario.  ... 
doi:10.1137/1.9781611973099.41 dblp:conf/soda/GoelKK12 fatcat:gzjojswvznbche36dlffke5rzi

Maximum Matching in Turnstile Streams [article]

Christian Konrad
2015 arXiv   pre-print
We consider the unweighted bipartite maximum matching problem in the one-pass turnstile streaming model where the input stream consists of edge insertions and deletions.  ...  Our lower bound result is proved in the simultaneous message model of communication and may be of independent interest.  ...  In this paper, we present a one-pass dynamic streaming algorithm for maximum bipartite matching and a space lower bound for streaming algorithms in the turnstile model, a slightly more general model than  ... 
arXiv:1505.01460v1 fatcat:qn76wml76baupgrrrsyz4es2r4

Maximum Matching in Turnstile Streams [chapter]

Christian Konrad
2015 Lecture Notes in Computer Science  
We consider the unweighted bipartite maximum matching problem in the one-pass turnstile streaming model where the input stream consists of edge insertions and deletions.  ...  Our lower bound result is proved in the simultaneous message model of communication and may be of independent interest.  ...  In this paper, we present a one-pass dynamic streaming algorithm for maximum bipartite matching and a space lower bound for streaming algorithms in the turnstile model, a slightly more general model than  ... 
doi:10.1007/978-3-662-48350-3_70 fatcat:cl2g52coqfewlpatbbxmvjusiy

Tight Bounds for Linear Sketches of Approximate Matchings [article]

Sepehr Assadi, Sanjeev Khanna, Yang Li, Grigory Yaroslavtsev
2015 arXiv   pre-print
We resolve the space complexity of linear sketches for approximating the maximum matching problem in dynamic graph streams where the stream may include both edge insertion and deletion.  ...  Specifically, we show that for any ϵ > 0, there exists a one-pass streaming algorithm, which only maintains a linear sketch of size Õ(n^2-3ϵ) bits and recovers an n^ϵ-approximate maximum matching in dynamic  ...  Acknowledgments We would like to thank Michael Kapralov and David Woodruff for helpful discussions.  ... 
arXiv:1505.01467v1 fatcat:rwpakvwnavaytlun6ohydvpuxm

Optimal Lower Bounds for Matching and Vertex Cover in Dynamic Graph Streams

Jacques Dark, Christian Konrad, Shubhangi Saraf
2020 Computational Complexity Conference  
In this paper, we give simple optimal lower bounds on the one-way two-party communication complexity of approximate Maximum Matching and Minimum Vertex Cover with deletions.  ...  [SODA 2016] gave an optimal space lower bound for insertion-deletion streaming algorithms for Maximum Matching via the simultaneous model of communication.  ...  Acknowledgements The authors are grateful for the numerous excellent comments and suggestions from an anonymous reviewer.  ... 
doi:10.4230/lipics.ccc.2020.30 dblp:conf/coco/DarkK20 fatcat:wdnnzaful5avfb7pexxkts3gqq

Optimal Lower Bounds for Matching and Vertex Cover in Dynamic Graph Streams [article]

Jacques Dark, Christian Konrad
2020 arXiv   pre-print
In this paper, we give simple optimal lower bounds on the one-way two-party communication complexity of approximate Maximum Matching and Minimum Vertex Cover with deletions.  ...  [SODA 2016] gave an optimal space lower bound for insertion-deletion streaming algorithms for Maximum Matching via the simultaneous model of communication.  ...  Indeed, the one-way two-party communication complexity of Maximum Matching without deletions has been addressed in [13] , and our result can therefore also be understood as a generalization of their model  ... 
arXiv:2005.11116v1 fatcat:ftmesaopxregvokon4gwq56b4i

Modified bipartite matching for multiobjective optimization

Fanglei Sun, Victor O. K. Li, Zhifeng Diao
2007 TENCON 2007 - 2007 IEEE Region 10 Conference  
In graph theory, the Hungarian algorithm can provide the maximum weighted bipartite matching for assignment problems.  ...  The simulation results show that MBM enjoys low computational complexity and maximizes the system capacity, while keeping the fairness among mobile users.  ...  In wireless MIMO communication systems based on spatial multiplexing, a data stream is split into multiple parallel substreams, and each substream is transmitted through one of the transmit antennas [  ... 
doi:10.1109/tencon.2007.4428865 fatcat:7dol74wv2fe6bdvgaof4ecpsvi

Semi-Streaming Algorithms for Annotated Graph Streams [article]

Justin Thaler
2015 arXiv   pre-print
On the negative side, we identify for the first time two natural graph problems (connectivity and bipartiteness in a certain edge update model) that can be solved in the standard semi-streaming model,  ...  On the positive side, we give semi-streaming annotation schemes for two dynamic graph problems that are intractable in the standard model: (exactly) counting triangles, and (exactly) computing maximum  ...  Acknowledgments The author is grateful to Graham Cormode, Amit Chakrabarti, Andrew McGregor, and Suresh Venkatasubramanian for many valuable discussions regarding this work.  ... 
arXiv:1407.3462v2 fatcat:4hblyqe66fhtvorkxmsnwro5je

Approximating Semi-matchings in Streaming and in Two-Party Communication

Christian Konrad, Adi Rosén
2016 ACM Transactions on Algorithms  
We study the streaming complexity and communication complexity of approximating unweighted semi-matchings.  ...  We present a deterministic one-pass streaming algorithm that for any 0 ≤ ≤ 1 uses spaceÕ(n 1+ ) and computes an O(n (1− )/2 )-approximation to the semi-matching problem.  ...  Acknowledgements We thank the reviewers for their comments which have improved the paper significantly.  ... 
doi:10.1145/2898960 fatcat:p5pevlqyrzadlivbbsd4pmty7i

Approximating Semi-matchings in Streaming and in Two-Party Communication [chapter]

Christian Konrad, Adi Rosén
2013 Lecture Notes in Computer Science  
We study the streaming complexity and communication complexity of approximating unweighted semi-matchings.  ...  We present a deterministic one-pass streaming algorithm that for any 0 ≤ ≤ 1 uses spaceÕ(n 1+ ) and computes an O(n (1− )/2 )-approximation to the semi-matching problem.  ...  Acknowledgements We thank the reviewers for their comments which have improved the paper significantly.  ... 
doi:10.1007/978-3-642-39206-1_54 fatcat:xaoxfmy7wbd3tnhwgpmdj32emi

Multiobjective optimized bipartite matching for resource allocation

Fanglei Sun, Victor O. K. Li, Zhifeng Diao
2007 2007 International Symposium on Communications and Information Technologies  
The Hungarian algorithm can provide the maximum weighted bipartite matching for assignment problems. However it can only solve the single objective weight optimization problem.  ...  In this paper, a modified bipartite matching (MBM) algorithm is proposed to solve the weighted bipartite matching problem with multiobjective optimization.  ...  In wireless multiple-input multiple-output (MIMO) communication systems based on spatial multiplexing, a data stream is split into multiple parallel substreams, and each substream is transmitted through  ... 
doi:10.1109/iscit.2007.4392101 fatcat:ue5ajzfx3rgtrp6sxtxj2d3paq

Semi-Streaming Algorithms for Annotated Graph Streams

Justin Thaler, Marc Herbstritt
2016 International Colloquium on Automata, Languages and Programming  
On the negative side, we identify for the first time two natural graph problems (connectivity and bipartiteness in a certain edge update model) that can be solved in the standard semi-streaming model,  ...  On the positive side, we give semi-streaming annotation schemes for two dynamic graph problems that are intractable in the standard model: (exactly) counting triangles, and (exactly) computing maximum  ...  Acknowledgments The author is grateful to Graham Cormode, Amit Chakrabarti, Andrew McGregor, and Suresh Venkatasubramanian for many valuable discussions regarding this work.  ... 
doi:10.4230/lipics.icalp.2016.59 dblp:conf/icalp/Thaler16a fatcat:wukacob35zctvcmjnvkbw6vrey

Streaming Verification of Graph Properties [article]

Amirali Abdullah, Samira Daruki, Chitradeep Dutta Roy, Suresh Venkatasubramanian
2016 arXiv   pre-print
In this paper, we present efficient streaming interactive proofs that can verify maximum matchings exactly. Our results cover all flavors of matchings (bipartite/non-bipartite and weighted).  ...  A computationally limited streaming client (the verifier) hands over a large data set to an untrusted server (the prover) in the cloud and the two parties run a protocol to confirm the correctness of result  ...  We now focus on the problem of certifying optimality of this matching. For this goal, we proceed by the standard LP-duality for bipartite maximum weight matching.  ... 
arXiv:1602.08162v2 fatcat:blq4gmv2qbgdxp7eeecgvveh2a

Approximating Semi-Matchings in Streaming and in Two-Party Communication [article]

Christian Konrad, Adi Rosén
2013 arXiv   pre-print
We study the communication complexity and streaming complexity of approximating unweighted semi-matchings.  ...  We present a deterministic one-pass streaming algorithm that for any 0 <= ϵ <= 1 uses space O(n^1+ϵ) and computes an O(n^(1-ϵ)/2)-approximation to the semi-matching problem.  ...  bound on the deterministic communication complexity we define a family of bipartite graphs.  ... 
arXiv:1304.6906v1 fatcat:eccz7mgeunddvlhn3guiesa7ly

Noisy Boolean Hidden Matching with Applications [article]

Michael Kapralov, Amulya Musipatla, Jakab Tardos, David P. Woodruff, Samson Zhou
2022 arXiv   pre-print
The one-way communication complexity of the Boolean Hidden Matching problem on a universe of size n is Θ(√(n)), resulting in Ω(√(n)) lower bounds for constant factor approximations to several of the aforementioned  ...  [STOC'07], has played an important role in the streaming lower bounds for graph problems such as triangle and subgraph counting, maximum matching, MAX-CUT, Schatten p-norm approximation, maximum acyclic  ...  CCF-181584 and a Simons Investigator Award.  ... 
arXiv:2107.02578v2 fatcat:6a24i67vi5fvpaoyv4y7u33rgu
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