A general framework for graph sparsification

Fung, Wai Shing; Hariharan, Ramesh; Harvey, Nicholas J. A.; Panigrahi, Debmalya

doi:10.1145/1993636.1993647

Cited by 69 publications

(15 citation statements)

References 32 publications

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“…Using the k-connectivity tester as a black-box we can also construct a (1 + )-sparsifier following the approach of Ahn et al [3]. The approach is based upon a result by Fung et al [20] that states that sampling each edge e with probability p e ≥ min 253λ…”

Section: Applications: Bipartiteness and Graph Sparsificationmentioning

confidence: 99%

Dynamic Graphs in the Sliding-Window Model

Crouch

McGregor

Stubbs

2013

Lecture Notes in Computer Science

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Abstract. We present the first algorithms for processing graphs in the slidingwindow model. The sliding window model, introduced by Datar et al. (SICOMP 2002), has become a popular model for processing infinite data streams in small space when older data items (i.e., those that predate a sliding window containing the most recent data items) are considered "stale" and should implicitly be ignored. While processing massive graph streams is an active area of research, it was hitherto unknown whether it was possible to analyze graphs in the slidingwindow model. We present an extensive set of positive results including algorithms for constructing basic graph synopses like combinatorial sparsifiers and spanners as well as approximating classic graph properties such as the size of a graph matching or minimum spanning tree.

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Section: Applications: Bipartiteness and Graph Sparsificationmentioning

confidence: 99%

Dynamic Graphs in the Sliding-Window Model

Crouch

McGregor

Stubbs

2013

Lecture Notes in Computer Science

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“…Purohit et al [21] proposed a merging based summarization algorithm which just maintains diffusion on a graph. There have been multiple studies on the related problem, such as graph sparsification [4] (where edges are removed in contrast to nodes being merged ).…”

Section: Related Workmentioning

confidence: 99%

MeiKe: Influence-based Communities in Networks

Zhang

Adhikari

Jan

et al. 2017

Proceedings of the 2017 SIAM International Conference on Data Mining

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Given a social network, how to find communities of nodes based on their diffusive characteristics? There exist two important types of nodes, for information propagation: nodes that are influential ("kernel nodes"), and nodes that serve as "bridges" to boost the diffusion ("media nodes"). How to find these nodes and uncover connections between them? In addition, it is also important to discover the hidden community structure of these nodes, which can help study their interactions, predict links and also understand the information flow in such networks.In this paper, we give an intuitive and novel optimization-based formulation for this task, which aims to discover media nodes as well as community structures of kernel nodes. We prove our task is computationally challenging, and develop an effective and practical algorithm MeiKe (pronounced as 'Mike'). It first obtains media nodes via a new successive summarization based approach, and then finds kernel nodes including their community structures. Experimental results show that MeiKe finds high-quality media and kernel communities which match our expectations and ground-truth (outperforming non-trivial baselines by 40% in F1-score). Our case studies also demonstrate the applicability of MeiKe on a variety of datasets.

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“…A spanner is a sparse subgraph that maintains the pairwise distances between all nodes within a multiplicative or additive factor. Fung et al [12] study the cut-sparsifier problem which asks for a sparse weighted subgraph such that the weight of all cuts is maintained within a small multiplicative factor. Graph sparsification for influence analysis has emerged as a new tool for analyzing large networks.…”

Section: Related Workmentioning

confidence: 99%

Fast influence-based coarsening for large networks

Purohit

Prakash

Kang

et al. 2014

Proceedings of the 20th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining

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Given a social network, can we quickly 'zoom-out' of the graph? Is there a smaller equivalent representation of the graph that preserves its propagation characteristics? Can we group nodes together based on their influence properties? These are important problems with applications to influence analysis, epidemiology and viral marketing applications.In this paper, we first formulate a novel Graph Coarsening Problem to find a succinct representation of any graph while preserving key characteristics for diffusion processes on that graph. We then provide a fast and effective near-linear-time (in nodes and edges) algorithm coarseNet for the same. Using extensive experiments on multiple real datasets, we demonstrate the quality and scalability of coarseNet, enabling us to reduce the graph by 90% in some cases without much loss of information. Finally we also show how our method can help in diverse applications like influence maximization and detecting patterns of propagation at the level of automatically created groups on real cascade data.

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A general framework for graph sparsification

Cited by 69 publications

References 32 publications

Dynamic Graphs in the Sliding-Window Model

Dynamic Graphs in the Sliding-Window Model

MeiKe: Influence-based Communities in Networks

Fast influence-based coarsening for large networks

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