Fully Dynamic Approximate k-Core Decomposition in Hypergraphs

In this article, we design algorithms to maintain approximate core values in dynamic hypergraphs. This notion has been well studied for normal graphs in both static and dynamic setting. We generalize the problem to hypergraphs when edges can be inserted or deleted by an adversary. We consider two dynamic scenarios. In the first case, there are only insertions; and in the second case, there can be both insertions and deletions. In either case, the update time is poly-logarithmic in the number of nodes, with the insertion-only case boasting a better approximation ratio. We also perform extensive experiments on large real-world datasets, which demonstrate the accuracy and efficiency of our algorithms.

[1]  Jeffrey Xu Yu,et al.  Efficient Core Maintenance in Large Dynamic Graphs , 2012, IEEE Transactions on Knowledge and Data Engineering.

[2]  Michalis Vazirgiannis,et al.  The core decomposition of networks: theory, algorithms and applications , 2019, The VLDB Journal.

[3]  Aristides Gionis,et al.  Density-friendly Graph Decomposition , 2015, WWW.

[4]  Stefan Wuchty,et al.  Peeling the yeast protein network , 2005, Proteomics.

[5]  Leng Min,et al.  An O(m) Algorithm for Cores Decomposition of Undirected Hypergraph , 2013 .

[6]  Chenzi Zhang,et al.  Spectral Properties of Hypergraph Laplacian and Approximation Algorithms , 2016, J. ACM.

[7]  Francesco De Pellegrini,et al.  General , 1895, The Social History of Alcohol Review.

[8]  Sergei Vassilvitskii,et al.  Densest Subgraph in Streaming and MapReduce , 2012, Proc. VLDB Endow..

[9]  Arnold I. Emerson,et al.  K-core decomposition of a protein domain co-occurrence network reveals lower cancer mutation rates for interior cores , 2015, Journal of Clinical Bioinformatics.

[10]  James Cheng,et al.  Efficient core decomposition in massive networks , 2011, 2011 IEEE 27th International Conference on Data Engineering.

[11]  Kun-Lung Wu,et al.  Streaming Algorithms for k-core Decomposition , 2013, Proc. VLDB Endow..

[12]  O. Sporns,et al.  Mapping the Structural Core of Human Cerebral Cortex , 2008, PLoS biology.

[13]  Yannis Stavrakas,et al.  Degeneracy-Based Real-Time Sub-Event Detection in Twitter Stream , 2015, ICWSM.

[14]  T.-H. Hubert Chan,et al.  Maintaining Densest Subsets Efficiently in Evolving Hypergraphs , 2017, CIKM.

[15]  Jia Wang,et al.  Truss Decomposition in Massive Networks , 2012, Proc. VLDB Endow..

[16]  Dimitrios M. Thilikos,et al.  Evaluating Cooperation in Communities with the k-Core Structure , 2011, 2011 International Conference on Advances in Social Networks Analysis and Mining.

[17]  Vladimir Batagelj,et al.  An O(m) Algorithm for Cores Decomposition of Networks , 2003, ArXiv.

[18]  S A R A H M E I K L E J O H N,et al.  A Fistful of Bitcoins Characterizing Payments Among Men with No Names , 2013 .

[19]  Shinichiro Wachi,et al.  Interactome-transcriptome analysis reveals the high centrality of genes differentially expressed in lung cancer tissues , 2005, Bioinform..

[20]  Moses Charikar,et al.  Greedy approximation algorithms for finding dense components in a graph , 2000, APPROX.

[21]  Stephen B. Seidman,et al.  Network structure and minimum degree , 1983 .

[22]  Alessandro Vespignani,et al.  Large scale networks fingerprinting and visualization using the k-core decomposition , 2005, NIPS.

[23]  Silvio Lattanzi,et al.  Efficient Densest Subgraph Computation in Evolving Graphs , 2015, WWW.

[24]  Charalampos E. Tsourakakis,et al.  Space- and Time-Efficient Algorithm for Maintaining Dense Subgraphs on One-Pass Dynamic Streams , 2015, STOC.

[25]  Jeffrey Xu Yu,et al.  I/O efficient Core Graph Decomposition at web scale , 2015, 2016 IEEE 32nd International Conference on Data Engineering (ICDE).

[26]  Dimitrios M. Thilikos,et al.  D-cores: measuring collaboration of directed graphs based on degeneracy , 2011, Knowledge and Information Systems.

[27]  Srinivasan Parthasarathy,et al.  Extracting Analyzing and Visualizing Triangle K-Core Motifs within Networks , 2012, 2012 IEEE 28th International Conference on Data Engineering.

[28]  Jeffrey Xu Yu,et al.  A Fast Order-Based Approach for Core Maintenance , 2016, 2017 IEEE 33rd International Conference on Data Engineering (ICDE).

[29]  T.-H. Hubert Chan,et al.  Large Scale Density-friendly Graph Decomposition via Convex Programming , 2017, WWW.

[30]  Alex Thomo,et al.  K-Core Decomposition of Large Networks on a Single PC , 2015, Proc. VLDB Endow..

[31]  Sabeur Aridhi,et al.  Distributed k-core decomposition and maintenance in large dynamic graphs , 2016, DEBS.