Streaming algorithms for k-core decomposition

Sarıyüce, Ahmet Erdem; Gedik, Buğra; Jacques-Silva, Gabriela; Wu, Kun-Lung; Çatalyürek, Ümit V.

doi:10.14778/2536336.2536344

Cited by 144 publications

(112 citation statements)

References 25 publications

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“…After deleing a node, the algorithm calls Algorithm 6 and Algorithm 7 to dynamically maintain the core numbers of the remaining nodes (lines 10-11). Notice that Algorithm 6 and Algorithm 7 generalize the core maintenance algorithm independently proposed in [16,20] to handle the case of node deletion 2 . Here we implement this core maintenance algorithm by dynamically updating the support of each node u (denoted by xu), which is defined as the number of neighbors whose updated core numbers are no smaller thancu.…”

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confidence: 99%

Influential community search in large networks

et al. 2015

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Community search is a problem of finding densely connected subgraphs that satisfy the query conditions in a network, which has attracted much attention in recent years. However, all the previous studies on community search do not consider the influence of a community. In this paper, we introduce a novel community model called k-influential community based on the concept of k-core, which can capture the influence of a community. Based on the new community model, we propose a linear-time online search algorithm to find the top-r k-influential communities in a network. To further speed up the influential community search algorithm, we devise a linear-space index structure which supports efficient search of the top-r k-influential communities in optimal time. We also propose an efficient algorithm to maintain the index when the network is frequently updated. We conduct extensive experiments on 7 real-world large networks, and the results demonstrate the efficiency and effectiveness of the proposed methods.

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confidence: 99%

Influential community search in large networks

et al. 2015

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“…While the literature has several efficient algorithms for core decomposition and truss decomposition, there has been limited work done in the area of streaming algorithms for these problems. Sariyuce et al [19] propose incremental algorithms for core decomposition for streaming graph data. Huang et al [12] present an algorithm for incrementally updating the truss decomposition for streaming graph data.…”

Section: Previous Workmentioning

confidence: 99%

Streaming and Batch Algorithms for Truss Decomposition

Jakkula

Karypis

2019

2019 First International Conference on Graph Computing (GC)

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Truss decomposition is a method used to analyze large sparse graphs in order to identify successively better connected subgraphs. Since in many domains the underlying graph changes over time, its associated truss decomposition needs to be updated as well. This work focuses on the problem of incrementally updating an existing truss decomposition and makes the following three significant contributions. First, it presents a theory that identifies how the truss decomposition can change as new edges get added. Second, it develops an efficient incremental algorithm that incorporates various optimizations to update the truss decomposition after every edge addition. These optimizations are designed to reduce the number of edges that are explored by the algorithm. Third, it extends this algorithm to batch updates (i.e., where the truss decomposition needs to be updated after a set of edges are added), which reduces the overall computations that need to be performed. We evaluated the performance of our algorithms on real-world datasets. Our incremental algorithm achieves over 250000× average speedup for inserting an edge in a graph with 10 million edges relative to the non-incremental algorithm. Further, our experiments on batch updates show that our batch algorithm consistently performs better than the incremental algorithm.

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“…Kumar et al [18] define an (i, j)-core which is a biclique with i vertices in one partition and j vertices in another partition, and present a dynamic algorithm for extracting non-overlapping sets of (i, j)-cores for interesting communities. Some other works on maintaining dense structures in dynamic graph include maintenance of k-cores [34], [21], k-truss [16], maximal clique [8] etc.…”

Section: Related Workmentioning

confidence: 99%

Incremental Maintenance of Maximal Bicliques in a Dynamic Bipartite Graph

Das

Tirthapura

2018

IEEE Trans. Multi-Scale Comp. Syst.

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We consider incremental maintenance of maximal bicliques from a dynamic bipartite graph that changes over time due to the addition of edges. When new edges are added to the graph, we seek to enumerate the change in the set of maximal bicliques, without enumerating the set of maximal bicliques that remain unaffected. The challenge is to enumerate the change without explicitly enumerating the set of all maximal bicliques. In this work, we present (1)~Near-tight bounds on the magnitude of change in the set of maximal bicliques of a graph, due to a change in the edge set, and an (2)~Incremental algorithm for enumerating the change in the set of maximal bicliques. For the case when a constant number of edges are added to the graph, our algorithm is "change-sensitive", i.e., its time complexity is proportional to the magnitude of change in the set of maximal bicliques. To our knowledge, this is the first incremental algorithm for enumerating maximal bicliques in a dynamic graph, with a provable performance guarantee. Experimental results show that its performance exceeds that of baseline implementations by orders of magnitude. RightsPersonal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Abstract-We consider incremental maintenance of maximal bicliques from a dynamic bipartite graph that changes over time due to the addition of edges. When new edges are added to the graph, we seek to enumerate the change in the set of maximal bicliques, without enumerating the set of maximal bicliques that remain unaffected. The challenge in an efficient algorithm is to enumerate the change without explicitly enumerating the set of all maximal bicliques. In this work, we present (1) Near-tight bounds on the magnitude of change in the set of maximal bicliques of a graph, due to a change in the edge set, and an (2) Incremental algorithm for enumerating the change in the set of maximal bicliques. For the case when a constant number of edges are added to the graph, our algorithm is "change-sensitive", i.e., its time complexity is proportional to the magnitude of change in the set of maximal bicliques. To our knowledge, this is the first incremental algorithm for enumerating maximal bicliques in a dynamic graph, with a provable performance guarantee. Our algorithm is easy to implement, and experimental results show that its performance exceeds that of baseline implementations by orders of magnitude.

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Streaming algorithms for k-core decomposition

Cited by 144 publications

References 25 publications

Influential community search in large networks

Influential community search in large networks

Streaming and Batch Algorithms for Truss Decomposition

Incremental Maintenance of Maximal Bicliques in a Dynamic Bipartite Graph

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