Abstract
Graph-structured databases have numerous recent applications including the Semantic Web, biological databases and XML, among many others. In this paper, we study the maintenance problem of a popular structural index, namely bisimulation, of a possibly cyclic data graph. In comparison, previous work mainly focuses on acyclic graphs. In the context of database applications, it is natural to compute minimal bisimulation with merging algorithms. First, we propose a maintenance algorithm for a minimal bisimulation of a cyclic graph, in the style of merging. Second, to prune the computation on non-bisimilar SCCs, we propose a feature-based optimization. The features are designed to be constructed and used more efficiently than bisimulation minimization. Third, we conduct an experimental study that verifies the effectiveness and efficiency of our algorithm. Our features-based optimization pruned 50% (on average) unnecessary bisimulation computation. Our experiment verifies that we extend the current state-of-the-art with a capability on handling cyclic graphs in maintenance of minimal bisimulation.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Batagelj, V., Mrvar, A.: Pajek datasets, http://vlado.fmf.uni-lj.si/pub/networks/data/
Buneman, P., Davidson, S.B., Fernandez, M.F., Suciu, D.: Adding structure to unstructured data. In: Afrati, F.N., Kolaitis, P.G. (eds.) ICDT 1997. LNCS, vol. 1186, Springer, Heidelberg (1996)
Buneman, P., Grohe, M., Koch, C.: Path queries on compressed XML. In: VLDB (2003)
Chen, Q., Lim, A., Ong, K.W.: D(k)-index: an adaptive structural summary for graph-structured data. In: SIGMOD (2003)
Deng, J., Choi, B., Xu, J., Bhowmick, S.S.: Optimizing incremental maintenance of minimal bisimulation of cyclic graphs. Technical report, HKBU (2010), http://www.comp.hkbu.edu/~jtdeng/techreport.pdf
Dovier, A., Piazza, C., Policriti, A.: An efficient algorithm for computing bisimulation equivalence. Theor. Comput. Sci. 311(1-3), 221–256 (2004)
Fisler, K., Vardi, M.Y.: Bisimulation minimization and symbolic model checking. Form. Methods Syst. Des. 21(1), 39–78 (2002)
Gleiss, P.M., Leydold, J., Stadler, P.F.: Circuit bases of strongly connected digraphs. Working Papers 01-10-056, Santa Fe Institute (2001), http://ideas.repec.org/p/wop/safiwp/01-10-056.html
Henzinger, M.R., King, V.: Maintaining minimum spanning trees in dynamic graphs. In: Degano, P., Gorrieri, R., Marchetti-Spaccamela, A. (eds.) ICALP 1997. LNCS, vol. 1256. Springer, Heidelberg (1997)
Kaushik, R., Bohannon, P., Naughton, J.F., Shenoy, P.: Updates for structure indexes. In: VLDB (2002)
Kaushik, R., Shenoy, P., Bohannon, P., Gudes, E.: Exploiting local similarity for indexing paths in graph-structured data. In: ICDE (2002)
Ke, Y., Hao, H., Ioana, S., Jun, Y.: Incremental maintenance of XML structural indexes. In: SIGMOD (2004)
Leskovec, J.: Stanford large network dataset collection, http://snap.stanford.edu/data
Li, H., Lee, M.L., Hsu, W., Cong, G.: An estimation system for XPath expressions. In: ICDE (2006)
Mendelzon, A.O., Wood, P.T.: Finding regular simple paths in graph databases. In: VLDB (1989)
Milner, R.: Communication and Concurrency. Prentice Hall, Englewood Cliffs (1989)
Milo, T., Suciu, D.: Index structures for path expressions. In: Beeri, C., Bruneman, P. (eds.) ICDT 1999. LNCS, vol. 1540, pp. 277–295. Springer, Heidelberg (1999)
Paige, R., Tarjan, R.E.: Three partition refinement algorithms. SIAM J. Comput. 16(6), 973–989 (1987)
Polyzotis, N., Garofalakis, M.: XCluster synopses for structured XML content. In: ICDE (2006)
Polyzotis, N., Garofalakis, M.: XSketch synopses for XML data graphs. ACM Trans. Database Syst. 31(3) (2006)
Saha, D.: An incremental bisimulation algorithm. In: Arvind, V., Prasad, S. (eds.) FSTTCS 2007. LNCS, vol. 4855, pp. 204–215. Springer, Heidelberg (2007)
Schmidt, A., Waas, F., Kersten, M., Carey, M.J., Manolescu, I., Busse, R.: XMark: A benchmark for XML data management. In: VLDB (2002)
Spiegel, J., Polyzotis, N.: Graph-based synopses for relational selectivity estimation. In: SIGMOD (2006)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Deng, J., Choi, B., Xu, J., Bhowmick, S.S. (2011). Optimizing Incremental Maintenance of Minimal Bisimulation of Cyclic Graphs. In: Yu, J.X., Kim, M.H., Unland, R. (eds) Database Systems for Advanced Applications. DASFAA 2011. Lecture Notes in Computer Science, vol 6587. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20149-3_39
Download citation
DOI: https://doi.org/10.1007/978-3-642-20149-3_39
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-20148-6
Online ISBN: 978-3-642-20149-3
eBook Packages: Computer ScienceComputer Science (R0)