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Efficient Densest Subgraph Computation in Evolving Graphs

Alessandro Epasto, Silvio Lattanzi, Mauro Sozio
2015 Proceedings of the 24th International Conference on World Wide Web - WWW '15  
Densest subgraph computation has emerged as an important primitive in a wide range of data analysis tasks such as community and event detection.  ...  We study the densest subgraph problem in the the dynamic graph model, for which we present the first scalable algorithm with provable guarantees.  ...  This is the case also for our larger datasets requiring billions of updates, allowing the computation of densest subgraphs in evolving graphs at these scales.  ... 
doi:10.1145/2736277.2741638 dblp:conf/www/EpastoLS15 fatcat:4544gmfvp5gijgpwoh4qjem57e

Discovery of Top-k Dense Subgraphs in Dynamic Graph Collections [chapter]

Elena Valari, Maria Kontaki, Apostolos N. Papadopoulos
2012 Lecture Notes in Computer Science  
We show that a significant number of exact density computations is avoided, resulting in efficient monitoring of the top-k dense subgraphs.  ...  In this work, we study the discovery of the top-k dense subgraphs in a set of graphs.  ...  The first one, involves the use of graph summaries in order to reduce the size of the graphs. This means that we are willing to sacrifice accuracy in favor of a more efficient computation.  ... 
doi:10.1007/978-3-642-31235-9_14 fatcat:de6fj2l2zjcj7cow2mk3ypmssy

Fully Dynamic Algorithm for Top-k Densest Subgraphs

Muhammad Anis Uddin Nasir, Aristides Gionis, Gianmarco De Francisci Morales, Sarunas Girdzijauskas
2017 Proceedings of the 2017 ACM on Conference on Information and Knowledge Management - CIKM '17  
In this paper, we study the top-k densest-subgraph problem in the sliding-window model and propose an efficient fully-dynamic algorithm.  ...  Given a large graph, the densest-subgraph problem asks to find a subgraph with maximum average degree.  ...  [14] proposed an efficient algorithm for computing the densest subgraph in the dynamic graph model [15] .  ... 
doi:10.1145/3132847.3132966 dblp:conf/cikm/NasirGMG17 fatcat:6iabcbzm4jhzff6z4prthlt44y

Scalable Large Near-Clique Detection in Large-Scale Networks via Sampling

Michael Mitzenmacher, Jakub Pachocki, Richard Peng, Charalampos Tsourakakis, Shen Chen Xu
2015 Proceedings of the 21th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining - KDD '15  
We also use our methods to study how the k-clique densest subgraphs change as a function of time in time-evolving networks for various small values of k.  ...  Extracting dense subgraphs from large graphs is a key primitive in a variety of graph mining applications, ranging from mining social networks and the Web graph to bioinformatics [41] .  ...  Acknowledgments Michael Mitzenmacher was supported in part by NSF grants IIS-0964473, CNS-1228598, and CCF-1320231. Jakub Pachocki and Shen Chen Xu were supported in part by NSF grant CCF-1065106.  ... 
doi:10.1145/2783258.2783385 dblp:conf/kdd/MitzenmacherPPT15 fatcat:gmn7sydbezhx3etolrwjameehu

Dense Subgraphs on Dynamic Networks [article]

Atish Das Sarma, Ashwin Lall, Danupon Nanongkai, Amitabh Trehan
2012 arXiv   pre-print
In distributed networks, it is often useful for the nodes to be aware of dense subgraphs, e.g., such a dense subgraph could reveal dense subtructures in otherwise sparse graphs (e.g. the World Wide Web  ...  Further, a special case of our results also gives the first fully decentralized approximation algorithms for densest and at-least-k-densest subgraph problems for static distributed graphs.  ...  Back to dynamic graphs, in addition to computing the (2 + ǫ)-approximated densest and (3 + ǫ)-approximated at-least-k-densest subgraphs, our algorithm can also maintain them at all times with high probability  ... 
arXiv:1208.1454v1 fatcat:f5lczar2e5eqbh7hztmlam5koe

Dense Subgraphs on Dynamic Networks [chapter]

Atish Das Sarma, Ashwin Lall, Danupon Nanongkai, Amitabh Trehan
2012 Lecture Notes in Computer Science  
In distributed networks, it is often useful for the nodes to be aware of dense subgraphs, e.g., such a dense subgraph could reveal dense subtructures in otherwise sparse graphs (e.g. the World Wide Web  ...  Further, a special case of our results also gives the first fully decentralized approximation algorithms for densest and at-least-k-densest subgraph problems for static distributed graphs.  ...  Back to dynamic graphs, in addition to computing the (2 + ǫ)-approximated densest and (3 + ǫ)-approximated at-least-k-densest subgraphs, our algorithm can also maintain them at all times with high probability  ... 
doi:10.1007/978-3-642-33651-5_11 fatcat:nyku5trs6jcoda5f64psim3pfe

Efficient algorithms for densest subgraph discovery

Yixiang Fang, Kaiqiang Yu, Reynold Cheng, Laks V. S. Lakshmanan, Xuemin Lin
2019 Proceedings of the VLDB Endowment  
Densest subgraph discovery (DSD) is a fundamental problem in graph mining.  ...  Given a graph G, DSD aims to find a subgraph D of G with the highest density (e.g., the number of edges over the number of vertices in D).  ...  Qin et al. developed solutions for finding the top-k locally densest subgraphs [54] . The EDS problem on evolving graphs is studied in [19] .  ... 
doi:10.14778/3342263.3342645 fatcat:egfsgtjzsnbsbkazs26vath2f4

Parallel Algorithms for Densest Subgraph Discovery Using Shared Memory Model [article]

B.D.M. De Zoysa, Y.A.M.M.A. Ali, M.D.I. Maduranga, Indika Perera, Saliya Ekanayake, Anil Vullikanti
2021 arXiv   pre-print
The problem of finding dense components of a graph is a widely explored area in data analysis, with diverse applications in fields and branches of study including community mining, spam detection, computer  ...  Furthermore, efforts were also steered towards devising a novel algorithm for the problem of densest subgraph discovery.  ...  Solutions for finding the top-k locally densest subgraphs were presented by Qin et al. [39] . Densest subgraph problem induced by evolving graphs is studied in [18] .  ... 
arXiv:2103.00154v1 fatcat:ghhhsir4jrajvoczhgyqht2dn4

Extracting dense communities from telecom call graphs

Vinayaka Pandit, Natwar Modani, Sougata Mukherjea, Amit A. Nanavati, Sambuddha Roy, Amit Agarwal
2008 2008 3rd International Conference on Communication Systems Software and Middleware and Workshops (COMSWARE '08)  
Our analysis is based on suitable algorithmic engineering of an approximation algorithm for the densest subgraph problem by Charikar [9].  ...  We present empirical results on massive graphs with millions of nodes and edges. We also discuss many open problems that are important in the context of analyzing telecom call graphs.  ...  Charikar [9] showed that the densest subgraph can be computed in polynomial time.  ... 
doi:10.1109/comswa.2008.4554383 dblp:conf/comsware/PanditMMNRA08 fatcat:hojfr7xs6nhvxnyzmf5a6uogii

The Wedge Picking Model: A Theoretical Analysis of Graph Evolution Caused by Triadic Closure and Algorithmic Implications

2021 Journal of Strategic Innovation and Sustainability  
We demonstrate the applicability of our method by applying it to the densest subgraph and tri-densest subgraph discovery problem.  ...  Social networks have become an inseparable part of human life and processing them in an efficient manner is a top priority in the study of networks.  ...  We formalize this observation in the next section for finding the densest subgraph in a dynamic graph.  ... 
doi:10.33423/jsis.v16i3.4442 fatcat:vvgbqy5olbhrlkr3dakoye2yfe

Finding Events in Temporal Networks: Segmentation Meets Densest-Subgraph Discovery

Polina Rozenshtein, Francesco Bonchi, Aristides Gionis, Mauro Sozio, Nikolaj Tatti
2018 2018 IEEE International Conference on Data Mining (ICDM)  
[21] , while a densest subgraph can be computed in real-world graphs containing up to tens of billions of edges [22] .  ...  In our case, we are additionally interested in understanding how the stories evolve over time.  ...  In the proof we show that Problem 5 is at least as hard as NP-complete densest-at-least-k-subgraph problem: given static graph G = (V , E ) and parameter k , find the densest subgraph with at least k nodes  ... 
doi:10.1109/icdm.2018.00055 dblp:conf/icdm/RozenshteinBGST18 fatcat:23nqc63dcnhsdhknaqb7pjs45q

Finding events in temporal networks: segmentation meets densest subgraph discovery

Polina Rozenshtein, Francesco Bonchi, Aristides Gionis, Mauro Sozio, Nikolaj Tatti
2019 Knowledge and Information Systems  
We adapt existing recent work on dynamic densest subgraph discovery and approximate dynamic programming to design a fast approximation algorithm.  ...  In this paper, we study the problem of discovering a timeline of events in a temporal network. We model events as dense subgraphs that occur within intervals of network activity.  ...  ] , while a densest subgraph can be computed in real-world graphs containing up to tens of billions of edges [17] .  ... 
doi:10.1007/s10115-019-01403-9 fatcat:s5axetnaqjdyreappwjglsfmoy

Finding events in temporal networks: Segmentation meets densest-subgraph discovery [article]

Polina Rozenshtein, Francesco Bonchi, Aristides Gionis, Mauro Sozio, Nikolaj Tatti
2018 arXiv   pre-print
In this paper we study the problem of discovering a timeline of events in a temporal network. We model events as dense subgraphs that occur within intervals of network activity.  ...  We adapt existing recent work on dynamic densest-subgraph discovery and approximate dynamic programming to design a fast approximation algorithm.  ...  a densest subgraph can be computed in real-world graphs containing up to tens of billions of edges [22] .  ... 
arXiv:1808.09317v2 fatcat:obb4ky2wcnfgvikqkmaldpgpgy

Towards Publish/Subscribe Functionality on Graphs

Lefteris Zervakis, Christos Tryfonopoulos, Vinay Setty, Stephan Seufert, Spiros Skiadopoulos
2016 International Conference on Extending Database Technology  
To this end, we design a proof-of-concept filtering algorithm for supporting structural matching of continuous graph queries against updates in the evolving graph and demonstrate the need for efficient  ...  To the best of our knowledge, this is the first work in the literature that considers supporting publish/subscribe in graphs; we focus specifically on massive and dynamically evolving graphs due to the  ...  Finally, we plan to develop a distributed solution for graph pub/sub that will fit naturally distributed evolving graphs and will be able to scale to massive amounts of data.  ... 
dblp:conf/edbt/ZervakisTSSS16 fatcat:4cmwhgevrvhqljmkgntzdcupaa

Revealing Cluster Structure of Graph by Path Following Replicator Dynamic [article]

Hairong Liu, Longin Jan Latecki, Shuicheng Yan
2013 arXiv   pre-print
We apply it to four important problems: maximum clique problem, densest k-subgraph problem, structure fitting, and discovery of high-density regions.  ...  In this paper, we propose a path following replicator dynamic, and investigate its potentials in uncovering the underlying cluster structure of a graph.  ...  To efficiently enumerate dense clusters on graph, a fast algorithm has been proposed in [6] , which evolves to a dense subgraph by iteratively shrinking and expansion.  ... 
arXiv:1303.2643v1 fatcat:ypyhgcdecfc7nmf2tyb3myopl4
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