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EM-FGS: Graph sparsification via faster semi-metric edges pruning

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Abstract

Graph sparsification is a useful approach for mining, analyzing, and visualizing large graphs. It simplifies the structure of a graph by pruning some of the edges while preserving the nodes. One well-known edge-removal technique is determination of a single shortest path between any pair of nodes to maintain the overall connectivity of the graph and remove the rest of the edges. Recently, a graph sparsification approach has been proposed that classifies the edges for removal according to metricity. Considering this classification system, a three-phase algorithm has been presented to prune the edges of each identified classification. The main bottleneck of the existing approach is the computational cost required for all three phases. To overcome these problems, we propose a new concept that generalizes the metricity of the edges to a uniform and homogeneous level. We also propose a new algorithm: edge metricity–based faster graph sparsification (EM-FGS), which utilizes edge weight as a constraint for effective pruning of the search space for shortest path computations. Our proposed approach is effective because we use the edge weight, which is a freely available intrinsic property of a graph, for edge-metricity identification. Our proposed approach improves the time complexity of existing methods from O(m ∗ n) + O(U3) to O(m ∗ log(n)). We evaluated our approach on publicly available real and synthetic graphs and improved the sequential algorithm’s execution time by a minimum of 125 times and the parallel algorithm’s runtime speed performance by 13 times while providing the same degree of accuracy.

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Notes

  1. https://networkdata.ics.uci.edu/data.php?id=109

  2. http://vlado.fmf.uni-lj.si/pub/networks/data/collab/netscience.htm

  3. http://snap.stanford.edu/data/ca-AstroPh.html

  4. http://www-personal.umich.edu/mejn/netdata/

  5. https://dblp.uni-trier.de/

  6. https://github.com/polinapolina/sparsification

References

  1. Ahn KJ, Guha S, McGregor A (2012) Graph sketches: sparsification, spanners, and subgraphs. In: Proceedings of the 31st ACM SIGMOD-SIGACT-SIGAI symposium on Principles of Database Systems. ACM, pp 5–14

  2. Kalavri V, Simas T, Logothetis D (2016) The shortest path is not always a straight line: leveraging semi-metricity in graph analysis. Proc VLDB Endowment 9(9):672–683

    Article  Google Scholar 

  3. Lancichinetti A, Fortunato S, Radicchi F (2008) Benchmark graphs for testing community detection algorithms. Phys Rev E 78(4):046110

    Article  Google Scholar 

  4. Aggarwal CC, Wang H (2010) A survey of clustering algorithms for graph data. In Managing and mining graph data. Springer, Boston, pp 275–301

  5. Sadhanala V, Wang Y-X, Tibshirani R (2016) Graph sparsification approaches for laplacian smoothing. In: Artificial Intelligence and Statistics, pp 1250–1259

  6. McGregor Andrew (2014) Graph stream algorithms: a survey. ACM SIGMOD Rec 43(1):9–20

    Article  Google Scholar 

  7. Benczúr AA, Karger DR (1996) Approximating st minimum cuts in Õ (n 2) time. In: Proceedings of the twenty-eighth annual ACM symposium on Theory of computing. ACM, pp 47–55

  8. Spielman DA, Teng S-H (2011) Spectral sparsification of graphs. SIAM J Comput 40(4):981–1025

    Article  MathSciNet  MATH  Google Scholar 

  9. Batson J, Spielman DA, Srivastava N, Teng S-H (2013) Spectral sparsification of graphs: theory and algorithms. Commun ACM 56(8):87–94

    Article  Google Scholar 

  10. Lee YT, Sun H (2015) Constructing linear-sized spectral sparsification in almost-linear time. In: IEEE 56th Annual Symposium on Foundations of Computer Science (FOCS).IEEE , pp 250–269

  11. Spielman DA, Srivastava N (2011) Graph sparsification by effective resistances. SIAM J Comput 40(6):1913–1926

    Article  MathSciNet  MATH  Google Scholar 

  12. Althöfer I, Das G, Dobkin D, Joseph D, Soares J (1993) On sparse spanners of weighted graphs. Discret Comput Geom 9(1):81–100

    Article  MathSciNet  MATH  Google Scholar 

  13. Peleg D, Schäffer AA (1989) Graph spanners. J Graph Theory 13(1):99–116

    Article  MathSciNet  MATH  Google Scholar 

  14. Baswana S, Sen S (2007) A simple and linear time randomized algorithm for computing sparse spanners in weighted graphs. Random Struct Algorithm 30(4):532–563

    Article  MathSciNet  MATH  Google Scholar 

  15. Roditty L, Zwick U (2004) On dynamic shortest paths problems. In: European Symposium on Algorithms. Springer, Berlin, pp 580–591

  16. Ruan N, Jin R, Huang Y (2011) Distance preserving graph simplification. In: 2011 IEEE 11Th International Conference on Data Mining (ICDM). IEEE, pp 1200–1205

  17. Gao J, Zhou J, Yu JX, Wang T (2014) Shortest path computing in relational dbmss. IEEE Trans knowl Data Eng 26(4):997–1011

    Article  Google Scholar 

  18. Anderson DG, Gu M, Melgaard C (2014) An Efficient Algorithm for Unweighted Spectral Graph Sparsification. arXiv:http://arXiv.org/abs/1410.4273

  19. Lindner G, Staudt CL, Hamann Mx, Meyerhenke H, Wagner D (2015) Structure-preserving sparsification of social networks. In: IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining (ASONAM). IEEE, pp 448–454

  20. Basuchowdhuri P, Sikdar S, Shreshtha S, Majumder S (2016) Detecting Community Structures in Social Networks by Graph Sparsification. In: Proceedings of the 3rd IKDD Conference on Data Science. ACM, pp 5

  21. Zhao Peixiang. (2015) Gsparsify Graph Motif Based Sparsification for Graph Clustering. In: Proceedings of the 24th ACM International on Conference on Information and Knowledge Management. ACM, pp 373–382

  22. Mathioudakis M, Bonchi F, Castillo C, Gionis A, Ukkonen A (2011) Sparsification of influence networks. In: Proceedings of the 17th ACM SIGKDD international conference on Knowledge discovery and data mining. ACM, pp 529–537

  23. Mallikarjuna K, Prasad KS, Subramanyam MV (2015) Compression of Noisy Images based on Sparsification using Discrete Rajan Transform. Int J Comput Appl 132(12):37–43

    Google Scholar 

  24. Maccioni A, Abadi DJ (2016) Scalable pattern matching over compressed graphs via dedensification. In: Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining. ACM, pp 1755–1764

  25. Charikar M, Leighton Tx, Li S, Moitra A (2010) Vertex sparsifiers and abstract rounding algorithms. In: 2010 51st Annual IEEE Symposium on Foundations of Computer Science (FOCS). IEEE, pp 265–274

  26. Ruan N, Jin R, Wang G, Huang K (2012) Network backbone discovery using edge clustering. arXiv:http://arXiv.org/abs/1202.1842

  27. Toivonen H, Mahler S, Zhou F (2010) A framework for path-oriented network simplification. In: International Symposium on Intelligent Data Analysis. Springer, Berlin, pp 220–231

  28. Zhou F, Mahler S, Toivonen H (2012) Simplification of networks by edge pruning. In: Bisociative Knowledge Discovery. Springer, Berlin, pp 179–198

  29. Parchas P, Papailiou N, Papadias D, Bonchi F (2018) Uncertain Graph Sparsification. IEEE Transactions on Knowledge and Data Engineering

  30. Feng Z (2016) Spectral graph sparsification in nearly-linear time leveraging efficient spectral perturbation analysis. In: Proceedings of the 53rd Annual Design Automation Conference. ACM, pp 57

  31. Hancock ER (2017) Shape Simplification Through Graph Sparsification. In: Graph-Based Representations in Pattern Recognition: 11th IAPR-TC-15 International Workshop, GbRPR 2017, Anacapri, Italy, Proceedings. Springer, vol 10310, pp 13

  32. Abraham I, Durfee D, Koutis I, Krinninger S, Peng R (2016) On fully dynamic graph sparsifiers. In: IEEE 57th Annual Symposium on Foundations of Computer Science (FOCS). IEEE, pp 335– 344

  33. Simas T, Rocha LM (2015) Distance closures on complex networks. Netw Sci 3(2):227–268

    Article  Google Scholar 

  34. Nawaz W, Khan K-U, Lee Y-K (2015) SPORE: Shortest path overlapped regions and confined traversals towards graph clustering. Appl Intell 42(1):208–232

    Article  Google Scholar 

  35. Akiba T, Iwata Y, Yoshida Y (2013) Fast exact shortest-path distance queries on large networks by pruned landmark labeling. In: Proceedings of the ACM SIGMOD International Conference on Management of Data. ACM, pp 349–360

  36. Belkin M, Niyogi P (2008) Towards a theoretical foundation for Laplacian-based manifold methods. J Comput Syst Sci 74(8):1289–1308

    Article  MathSciNet  MATH  Google Scholar 

  37. Gionis A, Rozenshtein P, Tatti N, Terzi E (2017) Community-aware network sparsification. In: Proceedings of the 2017 SIAM International Conference on Data Mining. Society for Industrial and Applied Mathematics, pp 426–434

  38. Feng Z (2018) Similarity-aware spectral sparsification by edge filtering. In 2018 55th ACM/ESDA/IEEE Design Automation Conference (DAC). IEEE, pp 1–6

  39. Zhao Z, Feng Z (2017) A spectral graph sparsification approach to scalable vectorless power grid integrity verification. In: Proceedings of the 54th Annual Design Automation Conference 2017. ACM, pp 68

  40. Li K, Zha H, Su Y, Yan X (2018) Unsupervised neural categorization for scientific publications. In: Proceedings of the 2018 SIAM International Conference on Data Mining. Society for Industrial and Applied Mathematics, pp 37–45

  41. Zhang C, Bi J, Xu S, Ramentol E, Fan G, Qiao B, Fujita H (2019) Multi-Imbalance: An open-source software for multi-class imbalance learning. Knowledge-Based Systems

  42. Fujita H, Cimr D (2019) Computer Aided detection for fibrillations and flutters using deep convolutional neural network. Inf Sci 486:231–239

    Article  Google Scholar 

  43. Zhang C, Liu C, Zhang X, Almpanidis G (2017) An up-to-date comparison of state-of-the-art classification algorithms. Expert Syst Appl 82:128–150

    Article  Google Scholar 

  44. Yuan H, Li J, Lai LL, Tang YY (2018) Graph-based multiple rank regression for image classification. Neurocomputing 315:394–404

    Article  Google Scholar 

Download references

Acknowledgements

This work was supported by the National Research Foundation of Korea (NRF) Grant funded by the Korea government (MEST) (No. 2018R1A2A2A05023669).

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Authors and Affiliations

  1. Department of Computer Science and Engineering, Kyung Hee University, 446-701, Seocheon-dong, Giheung-gu, Yongin-si, Gyeonggi-do, Republic of Korea

    Dolgorsuren Batjargal & Young-Koo Lee

  2. Department of Computer Science, National University of Computer and Emerging Sciences (FASTNUCES), Islamabad, Pakistan

    Kifayat Ullah Khan

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  1. Dolgorsuren Batjargal
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  3. Young-Koo Lee
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Correspondence to Young-Koo Lee.

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Batjargal, D., Khan, K.U. & Lee, YK. EM-FGS: Graph sparsification via faster semi-metric edges pruning. Appl Intell 49, 3731–3748 (2019). https://doi.org/10.1007/s10489-019-01479-4

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