Large Scale Density-friendly Graph Decomposition via Convex Programming
@article{Danisch2017LargeSD, title={Large Scale Density-friendly Graph Decomposition via Convex Programming}, author={Maximilien Danisch and T-H. Hubert Chan and Mauro Sozio}, journal={Proceedings of the 26th International Conference on World Wide Web}, year={2017} }
Algorithms for finding dense regions in an input graph have proved to be effective tools in graph mining and data analysis. Recently, Tatti and Gionis [WWW 2015] presented a novel graph decomposition (known as the locally-dense decomposition) that is similar to the well-known k-core decomposition, with the additional property that its components are arranged in order of their densities. Such a decomposition provides a valuable tool in graph mining. Unfortunately, their algorithm for computing…
26 Citations
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References
SHOWING 1-10 OF 48 REFERENCES
Denser than the densest subgraph: extracting optimal quasi-cliques with quality guarantees
- Computer Science, MathematicsKDD
- 2013
This paper defines a novel density function, which gives subgraphs of much higher quality than densest sub graphs: the graphs found by the method are compact, dense, and with smaller diameter.
Core decomposition of uncertain graphs
- Computer Science, MathematicsKDD
- 2014
It is shown that core decomposition of uncertain graphs can be carried out efficiently as well, and the definitions and methods are evaluated on a number of real-world datasets and applications, such as influence maximization and task-driven team formation.
Finding the Hierarchy of Dense Subgraphs using Nucleus Decompositions
- Computer ScienceWWW
- 2015
The nucleus decomposition of a graph is defined, which represents the graph as a forest of nuclei, and provably efficient algorithms for nucleus decompositions are given, and empirically evaluate their behavior in a variety of real graphs.
On Triangulation-based Dense Neighborhood Graphs Discovery
- Computer ScienceProc. VLDB Endow.
- 2010
A new definition of dense subgraph pattern, the DN -graph, which considers both the size of the substructure and the minimum level of interactions between any pair of the vertices, and can cope with semi-streaming environment where the graph edges cannot fit into main memory.
Finding Subgraphs with Maximum Total Density and Limited Overlap
- Computer Science, MathematicsWSDM
- 2015
This work defines and study a natural generalization of the densest subgraph problem, where the main goal is to find at most $k$ sub graphs with maximum total aggregate density, while satisfying an upper bound on the pairwise Jaccard coefficient between the sets of nodes of the subgraphs.
Greedy approximation algorithms for finding dense components in a graph
- Computer Science, MathematicsAPPROX
- 2000
This paper gives simple greedy approximation algorithms for these optimization problems of finding subgraphs maximizing these notions of density for undirected and directed graphs and answers an open question about the complexity of the optimization problem for directed graphs.
Space- and Time-Efficient Algorithm for Maintaining Dense Subgraphs on One-Pass Dynamic Streams
- Computer ScienceSTOC
- 2015
This paper develops an algorithm that is the first streaming algorithm that can maintain the densest subgraph in one pass and can be extended to a (2+ε)-approximation sublinear-time algorithm and a distributed-streaming algorithm.
Discovering Large Dense Subgraphs in Massive Graphs
- Computer Science, MathematicsVLDB
- 2005
D dense subgraph extraction is proposed as a useful primitive for spam detection, and its incorporation into the workflow of web search engines is discussed.
Local triangle-densest subgraphs
- Computer Science, Mathematics2016 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining (ASONAM)
- 2016
This work provides a formal definition for the classical densest subgraph problem and develops efficient algorithms with strong theoretical guarantees for finding subgraphs which are both compact and contain a large number of triangles.
The community-search problem and how to plan a successful cocktail party
- Computer ScienceKDD
- 2010
This paper studies a query-dependent variant of the community-detection problem, which it is called thecommunity-search problem: given a graph G, and a set of query nodes in the graph, it is sought to find a subgraph of G that contains the query nodes and it is densely connected, and develops an optimum greedy algorithm for this measure.