Finding lasting dense subgraphs

Semertzidis, Konstantinos; Pitoura, Evaggelia; Terzi, Evimaria; Tsaparas, Panayiotis

doi:10.1007/s10618-018-0602-x

Cited by 27 publications

(14 citation statements)

References 28 publications

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“…For temporal networks, to our knowledge, there are only few papers that consider the task of finding temporally coherent densest subgraphs. The most similar to our work aims at finding a heavy subgraph present in all, or k, snapshots [46]. Another related work focuses on finding a dense subgraph covered by k scattered intervals in a temporal network [44].…”

Section: Challenges and Contributionsmentioning

confidence: 94%

“…On the contrary, in this work we search for an interval partitioning and consider only graphs that are span continuous intervals. Other close works are by Jethava and Beerenwinkel [31] and Semertzidis et al [46]. However, these works consider a set of snapshots and search for a single heavy subgraph induced by one or several intervals.…”

Section: Case Studymentioning

confidence: 99%

“…However, these works consider a set of snapshots and search for a single heavy subgraph induced by one or several intervals. The work of Semertzidis et al [46] explores different formulations for the persistent heavy subgraph problem, including maximum average density, while Jethava and Beerenwinkel [31] focus solely on maximum average density.…”

Section: Case Studymentioning

confidence: 99%

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Finding events in temporal networks: segmentation meets densest subgraph discovery

et al. 2019

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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 formulate the event discovery task as an optimization problem, where we search for a partition of the network timeline into k non-overlapping intervals, such that the intervals span subgraphs with maximum total density. The output is a sequence of dense subgraphs along with corresponding time intervals, capturing the most interesting events during the network lifetime. A naïve solution to our optimization problem has polynomial but prohibitively high running time. We adapt existing recent work on dynamic densest subgraph discovery and approximate dynamic programming to design a fast approximation algorithm. Next, to ensure richer structure, we adjust the problem formulation to encourage coverage of a larger set of nodes. This problem is NP-hard; however, we show that on static graphs a simple greedy algorithm leads to approximate solution due to submodularity. We extend this greedy approach for temporal networks, but we lose the approximation guarantee in the process. Finally, we demonstrate empirically that our algorithms recover solutions with good quality.

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Section: Challenges and Contributionsmentioning

confidence: 94%

Section: Case Studymentioning

confidence: 99%

Section: Case Studymentioning

confidence: 99%

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Finding events in temporal networks: segmentation meets densest subgraph discovery

et al. 2019

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“…A common framework is (see, e.g., Charikar, Naamad, and Wu [34] and Semertzidis, Pitoura, Terzi, and Tsaparas [35]) when, instead of single graph, we are given a sequence of graphs on the same vertex set, and are looking for a subgraph, referred to as Densest Common Subgraph (DCS), that maximizes some aggregate measure of density over the graphs. The graph sequence may represent a temporal aspect, for example, a network that is changing in time.…”

Section: Dense Common Subgraphs In Multiple Graphsmentioning

confidence: 99%

“…Various results are presented about these objectives in [34,35], for example, the first two objectives lead to NP-hard optimization, while the other two are solvable in polynomial time.…”

Section: Dense Common Subgraphs In Multiple Graphsmentioning

confidence: 99%

In Search of the Densest Subgraph

Faragó

Mojaveri

2019

Algorithms

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In this survey paper, we review various concepts of graph density, as well as associated theorems and algorithms. Our goal is motivated by the fact that, in many applications, it is a key algorithmic task to extract a densest subgraph from an input graph, according to some appropriate definition of graph density. While this problem has been the subject of active research for over half of a century, with many proposed variants and solutions, new results still continuously emerge in the literature. This shows both the importance and the richness of the subject. We also identify some interesting open problems in the field.

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