Abstract
There is an ample body of recent research on indexing for structural graph queries. However, as verified by our experiments with a large number of random and scale-free graphs, there may be a great variation in the performances of indexes of graph queries. Unfortunately, the structures of graph indexes are often complex and ad-hoc, so deriving an accurate performance model is a daunting task. As a result, database practitioners may encounter difficulties in choosing the optimal index for their data graphs. In this paper, we address this problem by proposing a spectral decomposition method for predicting the relative performances of graph indexes. Specifically, given a graph, we compute its spectrum. We then propose a similarity function to compare the spectrums of graphs. We adopt a classification algorithm to build a model and a voting algorithm for predicting the optimal index. Our empirical studies on a large number of random and scale-free graphs, using four structurally distinguishable indexes, demonstrate that our spectral decomposition method is robust and almost always exhibits an accuracy of 70% or above.
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References
Agrawal, R., Borgida, A., Jagadish, H.V.: Efficient management of transitive relationships in large data and knowledge bases. In: SIGMOD, pp. 253–262 (1989)
Bramandia, R., Choi, B., Ng, W.K.: Incremental maintenance of 2-hop labeling of large graphs. TKDE 22, 682–698 (2010)
Brouwer, A.E., Haemers, W.H.: Spectra of Graphs. Springer (2012)
Cheng, J., Ke, Y., Ng, W., Lu, A.: Fg-index: towards verification-free query processing on graph databases. In: SIGMOD, pp. 857–872 (2007)
Chung, F.: Spectral Graph Theory. Conference Board of the Mathematical Sciences (1997)
Deng, J., Liu, F., Peng, Y., Choi, B., Xu, J.: Predicting the optimal ad-hoc index for reachability queries on graph databases. In: CIKM, pp. 2357–2360 (2011)
Dhillon, I.S., Guan, Y., Kulis, B.: Weighted graph cuts without eigenvectors: A multilevel approach. TPAMI 29, 1944–1957 (2007)
Hendrickson, B., Leland, R.: An improved spectral graph partitioning algorithm for mapping parallel computations. SIAM J. Sci. Comput. 16(2), 452–469 (1995)
Yellen, J., Gross, J.L.: Handbook of Graph Theory. CRC Press (2004)
Ng, A.Y., Jordan, M.I., Weiss, Y.: On spectral clustering: Analysis and an algorithm. In: NIPS, pp. 849–856. MIT Press (2001)
Peng, Y., Choi, B., Xu, J.: Selectivity estimation of twig queries on cyclic graphs. In: ICDE, pp. 960–971 (2011)
Schenkel, R., Theobald, A., Weikum, G.: Efficient creation and incremental maintenance of the hopi index for complex xml document collections. In: ICDE, pp. 360–371 (2005)
Song, L., Peng, Y., Choi, B., Xu, J., He, B.: Spectral decomposition for optimal graph index prediction. Technique Report (2012), http://www.comp.hkbu.edu.hk/~ypeng/papers/TechRep2012.pdf
Spielman, D.A.: Spectral graph theory and its applications. In: FOCS, pp. 29–38 (2007)
Spielman, D.A.: Spectral graph theory. In: Combinatorial Scientific Computing, pp. 1–23. Chapman and Hall/CRC Press (2011)
Yan, X., Han, J.: gspan: Graph-based substructure pattern mining. In: ICDM, pp. 721–724 (2002)
Yan, X., Yu, P.S., Han, J.: Graph indexing: a frequent structure-based approach. In: SIGMOD, pp. 335–346 (2004)
Yildirim, H., Chaoji, V., Zaki, M.J.: Grail: scalable reachability index for large graphs. PVLDB 3(1-2), 276–284 (2010)
Zhu, L., Choi, B., He, B., Yu, J.X., Ng, W.K.: A uniform framework for ad-hoc indexes to answer reachability queries on large graphs. In: Zhou, X., Yokota, H., Deng, K., Liu, Q. (eds.) DASFAA 2009. LNCS, vol. 5463, pp. 138–152. Springer, Heidelberg (2009)
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Song, L., Peng, Y., Choi, B., Xu, J., He, B. (2013). Spectral Decomposition for Optimal Graph Index Prediction. In: Pei, J., Tseng, V.S., Cao, L., Motoda, H., Xu, G. (eds) Advances in Knowledge Discovery and Data Mining. PAKDD 2013. Lecture Notes in Computer Science(), vol 7818. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-37453-1_16
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DOI: https://doi.org/10.1007/978-3-642-37453-1_16
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