ABSTRACT
Nowadays, many researchers and industry groups often suffer from the lack of a variety of large-scale real graphs. Although a lot of synthetic graph generation methods,(or models) such as RMAT and BA have been developed, their output graphs tend to be quite different from real-world graphs in terms of graph properties. There are a few graph upscaling methods such as Gscaler, they still fail to preserve important properties of the original graph and fail to upscale due to out of memory or too long runtime. In this paper, we propose a novel graph upscaling method called EvoGraph that can upscale the original graph with preserving its properties regardless of a scale factor. It determines and attaches new edges to the real graph using the preferential attachment mechanism in an effective and efficient way. Through extensive experiments, we have demonstrated that EvoGraph significantly outperforms the state-of-the-art graph upscaling method Gscaler in terms of preserving graph properties and performance measures such as runtime, memory usage, and scalability.
Supplemental Material
- Leman Akoglu and Christos Faloutsos . 2009. RTG: a recursive realistic graph generator using random typing Joint European Conference on Machine Learning and Knowledge Discovery in Databases. Springer, 13--28.Google Scholar
- Albert-László Barabási and Réka Albert . 1999. Emergence of scaling in random networks. science, Vol. 286, 5439 (1999), 509--512.Google Scholar
- Deepayan Chakrabarti, Yiping Zhan, and Christos Faloutsos . 2004. R-MAT: A Recursive Model for Graph Mining.. In SDM, Vol. Vol. 4. SIAM, 442--446.Google Scholar
- Avery Ching, Sergey Edunov, Maja Kabiljo, Dionysios Logothetis, and Sambavi Muthukrishnan . 2015. One trillion edges: graph processing at Facebook-scale. VLDB, Vol. 8, 12 (2015), 1804--1815. Google ScholarDigital Library
- Sergey Edunov, Dionysios Logothetis, Cheng Wang, Avery Ching, and Maja Kabiljo . 2016. Darwini: Generating realistic large-scale social graphs. arXiv preprint arXiv:1610.00664 (2016).Google Scholar
- Nicole Eikmeier and David F Gleich . 2017. Revisiting Power-law Distributions in Spectra of Real World Networks Proceedings of the 23rd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining. ACM, 817--826. Google ScholarDigital Library
- Paul ErdHos and Alfréd Rényi . 1959. On random graphs. Publicationes Mathematicae Debrecen Vol. 6 (1959), 290--297.Google Scholar
- Li Gao, Jia Wu, Hong Yang, Zhi Qiao, Chuan Zhou, and Yue Hu . 2016. Semi-Data-Driven Network Coarsening.. In IJCAI. 1483--1489. Google ScholarDigital Library
- Graph500 . 2017. Graph500 Benchmark. (2017). http://www.graph500.org/Google Scholar
- Ali Hadian, Sadegh Nobari, Behrooz Minaei-Bidgoli, and Qiang Qu . 2016. ROLL: Fast in-memory generation of gigantic scale-free networks Proceedings of the 2016 International Conference on Management of Data. ACM, 1829--1842. Google ScholarDigital Library
- Min-Soo Kim, Kyuhyeon An, Himchan Park, Hyunseok Seo, and Jinwook Kim . 2016. GTS: A Fast and Scalable Graph Processing Method based on Streaming Topology to GPUs Proceedings of the 2016 International Conference on Management of Data. ACM, 447--461. Google ScholarDigital Library
- Tamara G Kolda, Ali Pinar, Todd Plantenga, and Comandur Seshadhri . 2014. A scalable generative graph model with community structure. SIAM Journal on Scientific Computing Vol. 36, 5 (2014), C424--C452.Google ScholarDigital Library
- Jurij Leskovec, Deepayan Chakrabarti, Jon Kleinberg, and Christos Faloutsos . 2005 a. Realistic, mathematically tractable graph generation and evolution, using Kronecker multiplication. PKDD. Springer, 133--145.Google Scholar
- Jure Leskovec, Deepayan Chakrabarti, Jon Kleinberg, Christos Faloutsos, and Zoubin Ghahramani . 2010. Kronecker graphs: An approach to modeling networks. JMLR Vol. 11 (2010), 985--1042. Google ScholarDigital Library
- Jure Leskovec and Christos Faloutsos . 2006. Sampling from large graphs. In Proceedings of the 12th ACM SIGKDD international conference on Knowledge discovery and data mining. ACM, 631--636. Google ScholarDigital Library
- Jure Leskovec, Jon Kleinberg, and Christos Faloutsos . 2005 b. Graphs over time: densification laws, shrinking diameters and possible explanations Proceedings of the eleventh ACM SIGKDD international conference on Knowledge discovery in data mining. ACM, 177--187. Google ScholarDigital Library
- Steffen Maass, Changwoo Min, Sanidhya Kashyap, Woonhak Kang, Mohan Kumar, and Taesoo Kim . 2017. Mosaic: Processing a trillion-edge graph on a single machine Proceedings of the Twelfth European Conference on Computer Systems. ACM, 527--543. Google ScholarDigital Library
- Himchan Park and Min-Soo Kim . 2017. TrillionG: A Trillion-scale Synthetic Graph Generator using a Recursive Vector Model Proceedings of the 2017 ACM International Conference on Management of Data. ACM, 913--928. Google ScholarDigital Library
- SNAP . 2017. Stanford Network Analysis Project. (2017). http://snap.stanford.edu/Google Scholar
- Christian L Staudt, Aleksejs Sazonovs, and Henning Meyerhenke . 2014. Networkit: An interactive tool suite for high-performance network analysis. arXiv preprint arXiv:1403.3005 (2014).Google Scholar
- Duncan J Watts and Steven H Strogatz . 1998. Collective dynamics of 'small-world'networks. nature, Vol. 393, 6684 (1998), 440--442.Google Scholar
- Ming Wu, Fan Yang, Jilong Xue, Wencong Xiao, Youshan Miao, Lan Wei, Haoxiang Lin, Yafei Dai, and Lidong Zhou . 2015. G ra M: scaling graph computation to the trillions Proceedings of the Sixth ACM Symposium on Cloud Computing. ACM, 408--421. Google ScholarDigital Library
- JW Zhang, Anwesha Mal, and YC Tay . 2017. GscalerCloud: A Web-Based Graph Scaling Service. Data Engineering (ICDE), 2017 IEEE 33rd International Conference on. IEEE, 1391--1392.Google ScholarCross Ref
- JW Zhang and YC Tay . 2016 a. Dscaler: Synthetically scaling a given relational database. Proceedings of the VLDB Endowment Vol. 9, 14 (2016), 1671--1682. Google ScholarDigital Library
- JW Zhang and YC Tay . 2016 b. GSCALER: Synthetically Scaling A Given Graph.. EDBT. 53--64.Google Scholar
- Xiaowei Zhu, Wenguang Chen, Weimin Zheng, and Xiaosong Ma . 2016. Gemini: A Computation-Centric Distributed Graph Processing System. OSDI. 301--316. Google ScholarDigital Library
Recommendations
TrillionG: A Trillion-scale Synthetic Graph Generator using a Recursive Vector Model
SIGMOD '17: Proceedings of the 2017 ACM International Conference on Management of DataAs many applications encounter exponential growth in graph sizes, a fast and scalable graph generator has become more important than ever before due to lack of large-scale realistic graphs for evaluating the performance of graph processing methods. ...
Exhaustive Generation of k-Critical $${\mathcal H}$$-Free Graphs
WG 2016: Revised Selected Papers of the 42nd International Workshop on Graph-Theoretic Concepts in Computer Science - Volume 9941We describe an algorithm for generating all k-critical $${\mathcal H}$$-free graphs, based on a method of Hoíng et al. Using this algorithm, we prove that there are only finitely many 4-critical $$P_7,C_k$$-free graphs, for both $$k=4$$ and $$k=5$$. We ...
Exhaustive generation of k‐critical H‐free graphs
AbstractWe describe an algorithm for generating all k‐critical H‐free graphs, based on a method of Hoàng et al. A graph G is k‐critical H‐free if G is H‐free, k‐chromatic, and every H‐free proper subgraph of G is k−1‐colorable. Using this algorithm, we ...
Comments