Discovery of Top-k Dense Subgraphs in Dynamic Graph Collections

Valari, E.; Kontaki, Maria; Papadopoulos, Apostolos N.

doi:10.1007/978-3-642-31235-9_14

Cited by 21 publications

(13 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Valari et al [32] were the rst one to study the top-k densest subgraph problem for a stream consisting of a dynamic collection of graphs. ey proposed both an exact and an approximation algorithm for top-k densest subgraph discovery.…”

Section: Related Workmentioning

confidence: 99%

“…In applications, we are o en interested not only in one densest subgraph, but in the top-k. e top-k densest subgraphs can be vertex-disjoint, edge-disjoint, or overlapping [6,17]. Di erent objective functions and constraints give rise to di erent problem formulations [6,17,32]. In this work, we choose to maximize the sum of the densities of the k subgraphs in the solution.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Fully Dynamic Algorithm for Top- k Densest Subgraphs

Nasir

Gionis

Morales

et al. 2017

Proceedings of the 2017 ACM on Conference on Information and Knowledge Management

View full text Add to dashboard Cite

Given a large graph, the densest-subgraph problem asks to nd a subgraph with maximum average degree. When considering the top-k version of this problem, a naïve solution is to iteratively nd the densest subgraph and remove it in each iteration. However, such a solution is impractical due to high processing cost. e problem is further complicated when dealing with dynamic graphs, since adding or removing an edge requires re-running the algorithm. In this paper, we study the top-k densest-subgraph problem in the sliding-window model and propose an e cient fully-dynamic algorithm. e input of our algorithm consists of an edge stream, and the goal is to nd the node-disjoint subgraphs that maximize the sum of their densities. In contrast to existing state-of-the-art solutions that require iterating over the entire graph upon any update, our algorithm pro ts from the observation that updates only a ect a limited region of the graph. erefore, the top-k densest subgraphs are maintained by only applying local updates. We provide a theoretical analysis of the proposed algorithm and show empirically that the algorithm o en generates denser subgraphs than state-of-the-art competitors. Experiments show an improvement in e ciency of up to ve orders of magnitude compared to state-of-the-art solutions.

show abstract

Section: Related Workmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Fully Dynamic Algorithm for Top- k Densest Subgraphs

Nasir

Gionis

Morales

et al. 2017

Proceedings of the 2017 ACM on Conference on Information and Knowledge Management

View full text Add to dashboard Cite

show abstract

“…Unlike its singlesubgraph counterpart, the problem of finding a set of k dense subgraphs has received considerably less attention. Few authors [24,23] have discussed it, without providing any rigorous formulation of the problem. Instead they consider the most obvious heuristic that iteratively finds and removes the densest subgraph until k subgraphs have been found.…”

Section: Related Workmentioning

confidence: 99%

Finding Subgraphs with Maximum Total Density and Limited Overlap

Balalau

Bonchi

Chan

et al. 2015

Proceedings of the Eighth ACM International Conference on Web Search and Data Mining

View full text Add to dashboard Cite

Finding dense subgraphs in large graphs is a key primitive in a variety of real-world application domains, encompassing social network analytics, event detection, biology, and finance. In most such applications, one typically aims at finding several (possibly overlapping) dense subgraphs which might correspond to communities in social networks or interesting events. While a large amount of work is devoted to finding a single densest subgraph, perhaps surprisingly, the problem of finding several dense subgraphs with limited overlap has not been studied in a principled way, to the best of our knowledge. In this work we define and study a natural generalization of the densest subgraph problem, where the main goal is to find at most k subgraphs with maximum total aggregate density, while satisfying an upper bound on the pairwise Jaccard coefficient between the sets of nodes of the subgraphs. After showing that such a problem is NP-Hard, we devise an efficient algorithm that comes with provable guarantees in some cases of interest, as well as, an efficient practical heuristic. Our extensive evaluation on large realworld graphs confirms the efficiency and effectiveness of our algorithms.

show abstract

“…Along this direction, Chi et al 10 proposed a fast graph stream classification algorithm that uses discriminative clique hashing, which can be applicable for OLAP analysis over evolving complex networks. Furthermore, Valari et al 30 discovered top-k dense subgraphs in dynamic graph collections by means of both exact and approximate algorithms. As a preview, while these studies focus on graph mining, our mining algorithms in the current paper work on both graph-structured data and other non-graph data.…”

Section: Introductionmentioning

confidence: 99%

Effectively and Efficiently Mining Frequent Patterns from Dense Graph Streams on Disk

Braun

Cameron

Cuzzocrea

et al. 2014

Procedia Computer Science

View full text Add to dashboard Cite

In this paper, we focus on dense graph streams, which can be generated in various applications ranging from sensor networks to social networks, from bio-informatics to chemical informatics. We also investigate the problem of effectively and efficiently mining frequent patterns from such streaming data, in the targeted case of dealing with limited memory environments so that disk support is required. This setting occurs frequently (e.g., in mobile applications/systems) and is gaining momentum even in advanced computational settings where social networks are the main representative. Inspired by this problem, we propose (i) a specialized data structure called DSMatrix, which captures important data from dense graph streams onto the disk directly and (ii) stream mining algorithms that make use of such structure in order to mine frequent patterns effectively and efficiently. Experimental results clearly confirm the benefits of our approach.

show abstract

Discovery of Top-k Dense Subgraphs in Dynamic Graph Collections

Cited by 21 publications

References 15 publications

Fully Dynamic Algorithm for Top- k Densest Subgraphs

Fully Dynamic Algorithm for Top- k Densest Subgraphs

Finding Subgraphs with Maximum Total Density and Limited Overlap

Effectively and Efficiently Mining Frequent Patterns from Dense Graph Streams on Disk

Contact Info

Product

Resources

About