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Bipartite Matching in Nearly-linear Time on Moderately Dense Graphs
[article]
2021
arXiv
pre-print
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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]
2022
arXiv
pre-print
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2021 pre-print arXiv:2109.10163v1 fatcat:36r47pim4jeyneljvm26wtosia
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
2012
2012 IEEE 26th International Parallel and Distributed Processing Symposium
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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]
2018
arXiv
pre-print
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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]
2021
arXiv
pre-print
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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]
2014
arXiv
pre-print
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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
2015
Proceedings of the 24th International Conference on World Wide Web - WWW '15
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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
2012
2012 IEEE 12th International Conference on Data Mining
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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]
2013
arXiv
pre-print
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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]
2021
arXiv
pre-print
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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
2016
2016 IEEE 57th Annual Symposium on Foundations of Computer Science (FOCS)
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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
2007
Proceedings of the sixteenth ACM conference on Conference on information and knowledge management - CIKM '07
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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]
2013
arXiv
pre-print
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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
2013
2013 IEEE 54th Annual Symposium on Foundations of Computer Science
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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
2009
Proceedings of the eleventh international joint conference on Measurement and modeling of computer systems - SIGMETRICS '09
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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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