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Title: Incremental k-core decomposition: Algorithms and evaluation

A k-core of a graph is a maximal connected subgraph in which every vertex is connected to at least k vertices in the subgraph. k-core decomposition is often used in large-scale network analysis, such as community detection, protein function prediction, visualization, and solving NP-hard problems on real networks efficiently, like maximal clique finding. In many real-world applications, networks change over time. As a result, it is essential to develop efficient incremental algorithms for dynamic graph data. In this paper, we propose a suite of incremental k-core decomposition algorithms for dynamic graph data. These algorithms locate a small subgraph that is guaranteed to contain the list of vertices whose maximum k-core values have changed and efficiently process this subgraph to update the k-core decomposition. We present incremental algorithms for both insertion and deletion operations, and propose auxiliary vertex state maintenance techniques that can further accelerate these operations. Our results show a significant reduction in runtime compared to non-incremental alternatives. We illustrate the efficiency of our algorithms on different types of real and synthetic graphs, at varying scales. Furthermore, for a graph of 16 million vertices, we observe relative throughputs reaching a million times, relative to the non-incremental algorithms.
Authors:
 [1] ;  [2] ;  [3] ;  [3] ;  [4]
  1. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
  2. Bilkent Univ., Ankara (Turkey)
  3. IBM T.J. Watson Research Center, Yorktown Heights, NY (United States)
  4. The Ohio State Univ., Columbus, OH (United States)
Publication Date:
Report Number(s):
SAND2016-1193J
Journal ID: ISSN 1066-8888; 619260
Grant/Contract Number:
AC04-94AL85000
Type:
Accepted Manuscript
Journal Name:
The VLDB Journal
Additional Journal Information:
Journal Volume: 9; Journal Issue: 10; Journal ID: ISSN 1066-8888
Research Org:
Sandia National Lab. (SNL-CA), Livermore, CA (United States)
Sponsoring Org:
USDOE National Nuclear Security Administration (NNSA)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING
OSTI Identifier:
1239351

Sariyuce, Ahmet Erdem, Gedik, Bugra, Jacques-SIlva, Gabriela, Wu, Kun -Lung, and Catalyurek, Umit V. Incremental k-core decomposition: Algorithms and evaluation. United States: N. p., Web. doi:10.1007/s00778-016-0423-8.
Sariyuce, Ahmet Erdem, Gedik, Bugra, Jacques-SIlva, Gabriela, Wu, Kun -Lung, & Catalyurek, Umit V. Incremental k-core decomposition: Algorithms and evaluation. United States. doi:10.1007/s00778-016-0423-8.
Sariyuce, Ahmet Erdem, Gedik, Bugra, Jacques-SIlva, Gabriela, Wu, Kun -Lung, and Catalyurek, Umit V. 2016. "Incremental k-core decomposition: Algorithms and evaluation". United States. doi:10.1007/s00778-016-0423-8. https://www.osti.gov/servlets/purl/1239351.
@article{osti_1239351,
title = {Incremental k-core decomposition: Algorithms and evaluation},
author = {Sariyuce, Ahmet Erdem and Gedik, Bugra and Jacques-SIlva, Gabriela and Wu, Kun -Lung and Catalyurek, Umit V.},
abstractNote = {A k-core of a graph is a maximal connected subgraph in which every vertex is connected to at least k vertices in the subgraph. k-core decomposition is often used in large-scale network analysis, such as community detection, protein function prediction, visualization, and solving NP-hard problems on real networks efficiently, like maximal clique finding. In many real-world applications, networks change over time. As a result, it is essential to develop efficient incremental algorithms for dynamic graph data. In this paper, we propose a suite of incremental k-core decomposition algorithms for dynamic graph data. These algorithms locate a small subgraph that is guaranteed to contain the list of vertices whose maximum k-core values have changed and efficiently process this subgraph to update the k-core decomposition. We present incremental algorithms for both insertion and deletion operations, and propose auxiliary vertex state maintenance techniques that can further accelerate these operations. Our results show a significant reduction in runtime compared to non-incremental alternatives. We illustrate the efficiency of our algorithms on different types of real and synthetic graphs, at varying scales. Furthermore, for a graph of 16 million vertices, we observe relative throughputs reaching a million times, relative to the non-incremental algorithms.},
doi = {10.1007/s00778-016-0423-8},
journal = {The VLDB Journal},
number = 10,
volume = 9,
place = {United States},
year = {2016},
month = {2}
}