# 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

Flowless: Extracting Densest Subgraphs Without Flow Computations

- Computer ScienceWWW
- 2020

Greedy++ is an iterative peeling algorithm that improves upon the performance of Charikar’s greedy algorithm significantly and is more robust against the structural heterogeneities in real-world datasets.

Efficient Algorithms for Densest Subgraph Discovery

- Computer ScienceProc. VLDB Endow.
- 2019

The main observation is that a densest subgraph can be accurately found through a k-core (a kind of dense subgraph of G), with theoretical guarantees, and efficient exact and approximation solutions for DSD are developed.

Distributed Approximate k-Core Decomposition and Min-Max Edge Orientation: Breaking the Diameter Barrier

- Computer Science2019 IEEE International Parallel and Distributed Processing Symposium (IPDPS)
- 2019

A primal-dual algorithm for computing the coreness values of the nodes in the underlying graph, as well as a 2(1+ε)-approximation algorithm for the min-max edge orientation problem, where the goal is to orient the edges so as to minimize the maximum weighted in-degree.

Efficient Algorithms for Densest Subgraph Discovery on Large Directed Graphs

- Computer ScienceSIGMOD Conference
- 2020

The notion of [ x, y]-core is introduced, which is a dense subgraph for G, and it is shown that the densest subgraph can be accurately located through the [x, y]core with theoretical guarantees.

Listing k-cliques in Sparse Real-World Graphs*

- Computer ScienceWWW
- 2018

This work revisits the iconic algorithm of Chiba and Nishizeki and develops the most efficient parallel algorithm for list all k-cliques in graphs containing up to tens of millions of edges, which is faster than state-of-the-art algorithms, while boasting an excellent degree of parallelism.

KClist++: A Simple Algorithm for Finding k-Clique Densest Subgraphs in Large Graphs

- Computer ScienceProc. VLDB Endow.
- 2020

A surprisingly simple procedure is given that can be employed to find the maximal k-clique densest subgraph in large-real world graphs and is complemented with an extensive experimental evaluation showing the effectiveness of the approach in large real-world graphs.

The core decomposition of networks: theory, algorithms and applications

- Computer ScienceThe VLDB Journal
- 2019

In this survey, an in-depth discussion of core decomposition is performed, focusing mainly on the basic theory and fundamental concepts, the algorithmic techniques proposed for computing it efficiently under different settings, and the applications that can benefit significantly from it.

Efficient Directed Densest Subgraph Discovery

- Computer ScienceSIGMOD Rec.
- 2021

An efficient and scalable DDS solution is developed based on the notion of [x, y]-core, which is a dense subgraph for G, and it is shown that the densest subgraph can be accurately located through the [ x, y]core with theoretical guarantees.

On Directed Densest Subgraph Discovery

- Computer Science, MathematicsACM Trans. Database Syst.
- 2021

An efficient and scalable DDS solution is developed based on the notion of [x, y]-core, which is a dense subgraph for G, and it is shown that the densest subgraph can be accurately located through the [ x, y]core with theoretical guarantees.

Deconstruct Densest Subgraphs

- MathematicsWWW
- 2020

It is shown that the structures, the relationships and the distributions of all the densest subgraphs of a graph G can be encoded in O(L) space in an index called the ds-Index, where L denotes the maximum output size of a densmost subgraph of G.

## 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.