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Bipartite Matching in Nearly-linear Time on Moderately Dense Graphs [article]

Jan van den Brand, Yin-Tat Lee, Danupon Nanongkai, Richard Peng, Thatchaphol Saranurak, Aaron Sidford, Zhao Song, Di Wang
2021 arXiv   pre-print
For maximum cardinality bipartite matching on moderately dense graphs, i.e. m = Ω(n^1.5), our algorithm runs in time nearly linear in the input size and constitutes the first improvement over the classic  ...  We present an Õ(m+n^1.5)-time randomized algorithm for maximum cardinality bipartite matching and related problems (e.g. transshipment, negative-weight shortest paths, and optimal transport) on m-edge,  ...  Acknowledgments We thank Yang Liu for helpful conversations, feedback on earlier drafts of the paper, and suggesting Lemma 4.23 and its application.  ... 
arXiv:2009.01802v2 fatcat:ja5h7w3u45hizldeeuzr5oseza

On dispersability of some circulant graphs [article]

Samuel S. Joslin, Paul C. Kainen, Shannon Overbay
2022 arXiv   pre-print
The matching book thickness mbt(G) of a graph G is the least number of pages in a book embedding such that each page is a matching; G is dispersable if mbt(G) = Δ(G), where Δ is the maximum degree.  ...  Recently, Alam et al disproved the 40-year-old Bernhart-Kainen conjecture that all regular bipartite graphs are dispersable, motivating further work on dispersability.  ...  In particular, if the target value of ∆ for bipartite graphs or ∆+1 for non-bipartite graphs is reached, then we know optimal matching book thickness has been achieved.  ... 
arXiv:2109.10163v2 fatcat:lnxkshg45jgitbazx2qjk2kc3m

Multithreaded Algorithms for Maxmum Matching in Bipartite Graphs

Ariful Azad, Mahantesh Halappanavar, Sivasankaran Rajamanickam, Erik G. Boman, Arif Khan, Alex Pothen
2012 2012 IEEE 26th International Parallel and Distributed Processing Symposium  
We design, implement, and evaluate algorithms for computing a matching of maximum cardinality in a bipartite graph on multicore and massively multithreaded computers.  ...  Recent work on serial algorithms for the matching problem has shown that their performance is sensitive to the order in which the vertices are processed for matching.  ...  For many graphs we obtain nearly linear speed-ups.  ... 
doi:10.1109/ipdps.2012.82 dblp:conf/ipps/AzadHRBKP12 fatcat:t24ulqe2ajggleqxtwjh3lix2i

An Experimental Study of Algorithms for Online Bipartite Matching [article]

Allan Borodin, Christodoulos Karavasilis, Denis Pankratov
2018 arXiv   pre-print
We are also interested in whether preprocessing times and implementation difficulties that are introduced by these algorithms are justified in practice.  ...  Greediness is by far the most important property of online algorithms for bipartite matching.  ...  Using the simplex method from the GNU Linear Programming Toolkit even with moderately dense graphs (e.g., d = 100) already results in excessive runtimes and in memory consumption of over 6GB.  ... 
arXiv:1808.04863v1 fatcat:2cxtryl53fdvjjwcprhxswovdm

Breaking the n-Pass Barrier: A Streaming Algorithm for Maximum Weight Bipartite Matching [article]

S. Cliff Liu, Zhao Song, Hengjie Zhang
2021 arXiv   pre-print
Given a weighted bipartite graph with n vertices and m edges, the maximum weight bipartite matching problem is to find a set of vertex-disjoint edges with the maximum weight.  ...  To the best of our knowledge, this is the first work that implements the SDD solvers and IPMs in the streaming model in O(n) spaces for graph matrices; previous IPM algorithms only focus on optimizing  ...  For moderately dense graph, a better algorithm is given in [BLN + 20] very recently, which runs in O(m + n 1.5 ) time and takes Ω(m) space.  ... 
arXiv:2009.06106v2 fatcat:bkjmromopvg6zfubstu444dg2e

Recommendation Subgraphs for Web Discovery [article]

Arda Antikacioglu, R. Ravi, Srinath Srihdar
2014 arXiv   pre-print
We formulate this as a natural graph optimization problem which in its simplest case, reduces to a bipartite matching problem.  ...  In practice, solving these matching problems requires superlinear time and is not scalable.  ...  Graph matching algorithms require linear memory and super-linear run-time which does not scale well.  ... 
arXiv:1409.2042v1 fatcat:43duhly6w5cebdffoot5rp2pz4

Recommendation Subgraphs for Web Discovery

Arda Antikacioglu, R. Ravi, Srinath Sridhar
2015 Proceedings of the 24th International Conference on World Wide Web - WWW '15  
Such sites typically contain a set of recommendations on every product page that enables visitors to easily navigate the website.  ...  These recommendations are essentially universally present on all e-commerce websites. Choosing an appropriate set of recommendations at *  ...  Graph matching algorithms require linear memory and super-linear run-time which does not scale well.  ... 
doi:10.1145/2736277.2741680 dblp:conf/www/AntikaciogluRS15 fatcat:4luytbwt5vaefc5h3lmhadizru

A General and Scalable Approach to Mixed Membership Clustering

Frank Lin, William W. Cohen
2012 2012 IEEE 12th International Conference on Data Mining  
Spectral clustering methods are elegant and effective graph-based node clustering methods, but they do not allow mixed membership clustering.  ...  Experimental results show the proposed approach improves substantially in mixed membership clustering tasks over node clustering methods.  ...  However, a simple and efficient "trick" can be applied to obtain a solution with time and space complexity linear to the size of the input, based on a couple of observations: 1) The (likely) dense similarity  ... 
doi:10.1109/icdm.2012.166 dblp:conf/icdm/LinC12 fatcat:agruk4h4anc3zgflxiyf54vdye

Navigating Central Path with Electrical Flows: from Flows to Matchings, and Back [article]

Aleksander Madry
2013 arXiv   pre-print
By well-known reductions, this also establishes an Õ(m^10/7)-time algorithm for the maximum-cardinality bipartite matching problem.  ...  We present an Õ(m^10/7)=Õ(m^1.43)-time algorithm for the maximum s-t flow and the minimum s-t cut problems in directed graphs with unit capacities.  ...  We also thank Monika Henziger, Satish Rao, and Jens Vygen for useful feedback on the manuscript.  ... 
arXiv:1307.2205v3 fatcat:gdo5xowkgrasrkyjh56gup2hau

Faster Matchings via Learned Duals [article]

Michael Dinitz, Sungjin Im, Thomas Lavastida, Benjamin Moseley, Sergei Vassilvitskii
2021 arXiv   pre-print
We consider one of the most important primitives in combinatorial optimization: weighted bipartite matching and its generalization to b-matching.  ...  We validate our theoretical findings through experiments on both real and synthetic data. As a result we give a rigorous, practical, and empirically effective method to compute bipartite matchings.  ...  The following lemma is well-known. √ n · m) [29] , which is still state-of-the-art for general bipartite graphs. For moderately dense graphs, a recent result by van den Brand et al.  ... 
arXiv:2107.09770v1 fatcat:yoa4cdwcx5exldrye3mk3kr4vm

Computing Maximum Flow with Augmenting Electrical Flows

Aleksander Madry
2016 2016 IEEE 57th Annual Symposium on Foundations of Computer Science (FOCS)  
Already in 1931, König [32] and Egerváry [13] provided first constructive characterization of maximum matchings in bipartite graphs.  ...  Finally, a lot of developments has been done in the context of the (maximum-cardinality) matching problem in general, i.e., not necessarily bipartite, graphs.  ...  We are grateful to Michael Cohen, Slobodan Mitrović, Dimitris Tsipras, and Adrian Vladu for a number of helpful discussions on this topic.  ... 
doi:10.1109/focs.2016.70 dblp:conf/focs/Madry16 fatcat:gqoct5u4vncgrafp5ndz6uz26a

Finding dense and isolated submarkets in a sponsored search spending graph

Kevin J. Lang, Reid Andersen
2007 Proceedings of the sixteenth ACM conference on Conference on information and knowledge management - CIKM '07  
We apply our algorithm to find submarkets that are both dense and isolated in a large spending graph from Yahoo! sponsored search.  ...  The problem of finding the densest subgraph (the subgraph of highest average degree) can be solved in polynomial time [16] , or approximated within a factor of two in roughly linear time [21] .  ...  The task that motivated this research is to find a moderately sized subgraph of the spending graph that is both dense, containing a large amount of money M (H) for its size, and isolated, having a small  ... 
doi:10.1145/1321440.1321526 dblp:conf/cikm/LangA07 fatcat:g7hlpyngwndodguksw4xgr6ma4

Kidney Exchange in Dynamic Sparse Heterogenous Pools [article]

Itai Ashlagi and Patrick Jaillet and Vahideh H. Manshadi
2013 arXiv   pre-print
Finally, a significant increase of matches can be obtained by using even one non-simultaneous chain while still matching in an online fashion.  ...  We find that if only 2-way cycles are conducted, in order to gain a significant amount of matches over the online scenario (matching each time a new incompatible pair joins the pool) the waiting period  ...  Chunk matching in moderately dense graphs We have studied so far dense graphs (in Lemma 2.1) and sparse graphs where the probability for connecting to an H node is c n .  ... 
arXiv:1301.3509v2 fatcat:wywn6yrg2fet5a2hscwbio33jy

Navigating Central Path with Electrical Flows: From Flows to Matchings, and Back

Aleksander Madry
2013 2013 IEEE 54th Annual Symposium on Foundations of Computer Science  
This reduction is then composed with the recent sublinear-time algorithm for finding perfect matchings in regular graphs of Goel et al.  ...  We present an O(m 10 7 ) = O(m 1.43 )-time 1 algorithm for the maximum s-t flow and the minimum s-t cut problems in directed graphs with unit capacities.  ...  We also thank Monika Henziger, Satish Rao, and Jens Vygen for useful feedback on the manuscript.  ... 
doi:10.1109/focs.2013.35 dblp:conf/focs/Madry13 fatcat:cr3of5bblnhrxkr2e4paglyx6a

Unveiling core network-wide communication patterns through application traffic activity graph decomposition

Yu Jin, Esam Sharafuddin, Zhi-Li Zhang
2009 Proceedings of the eleventh international joint conference on Measurement and modeling of computer systems - SIGMETRICS '09  
In order to analyze and characterize these TAGs, we propose a novel statistical traffic graph decomposition technique based on orthogonal nonnegative matrix tri-factorization (tNMF) to decompose and extract  ...  In this paper, we study the network traffic behaviors using traffic activity graphs (TAGs), which capture the interactions among hosts engaging in certain types of communications and their collective behavior  ...  The resulting graph is not strictly bipartite, but nearly so, as there are only 10 (0.1%) IP addresses that appear as both source and destination in the flows. In  ... 
doi:10.1145/1555349.1555356 dblp:conf/sigmetrics/JinSZ09 fatcat:4i57fbtnfjevno4ggmxuhistfu
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