Hasan Jamil
ABSTRACT
Graphs and trees play a major role in many applications including social networks, internet management, science, and business. Yet, there remains a serious lack of tools for graph data management, analysis and querying. Systems that rely on non-traditional complex relationships among objects naturally invite a fresh look at data models and query languages suitable for applications that require graphs as first class citizens. In this paper, we propose a new data model for the storage and management of graph objects, and present a heuristic algorithm to efficiently compute subgraph isomorphic queries, and show that the same algorithm can be adapted to perform a wide range of graph queries. We rely upon the introduction of the idea of structural unification, a novel graph representation based on minimum structures, and an indexing mechanism for storing minimum graph structures. We experimentally show that our approach yields significant speed up over the two leading subgraph isomorphism algorithms Ullmann and VFLib.
- DroID. http://www.droidb.org.Google Scholar
- Formula to Compute the Number of Possible Networks. http://www.research.att.com/~njas/sequences/A000088.Google Scholar
- KEGG. http://www.genome.jp/kegg/.Google Scholar
- Reactome. http://www.reactome.org/.Google Scholar
- S. Brin and L. Page. The anatomy of a large-scale hypertextual web search engine. In WWW, 1998. Google ScholarDigital Library
- J. Cheng, Y. Ke, W. Ng, and A. Lu. FG-Index: towards verification-free query processing on graph databases. In SIGMOD, pages 857--872, 2007. Google ScholarDigital Library
- L. P. Cordella, P. Foggia, C. Sansone, and M. Vento. An improved algorithm for matching large graphs. In 3rd IAPR-TC15 Workshop on Graph-based Representations in Pattern Recognition, pages 149--159, Cuen, 2001.Google Scholar
- R. Giugno and D. Shasha. GraphGrep: A fast and universal method for querying graphs. In ICPR, volume 2, pages 112--115, 2002.Google ScholarCross Ref
- M. Gori, M. Maggini, and L. Sarti. Exact and approximate graph matching using random walks. IEEE TPAMI, 27: 1100--1111, 2005. Google ScholarDigital Library
- H. He and A. K. Singh. Graphs-at-a-time: query language and access methods for graph databases. In SIGMOD Conference, pages 405--418, 2008. Google ScholarDigital Library
- H. M. Jamil and L. Lakshmanan. A declarative semantics for behavioral inheritance and conflict resolution. In ILPS, 1995.Google Scholar
- H. Jiang, H. Wang, P. S. Yu, and S. Zhou. GString: A novel approach for efficient search in graph databases. In ICDE, pages 566--575, 2007.Google ScholarCross Ref
- M. Koyuturk, Y. Kim, S. Subramanium, W. Szpankowski, and A. Grama. Detecting conserved interaction patterns in biological networks. Journal of Computational Biology, 3(7): 1299U-1322, 2006.Google ScholarCross Ref
- R Development Core Team. R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria, 2009. ISBN 3-900051-07-0.Google Scholar
- E. Rich and K. Knight, editors. Artificial Intelligence. McGraw Hill Higher Education; 2nd edition, 1991. Google ScholarDigital Library
- S. Saito, S. Aburatani, and K. Horimoto. Network evaluation from the consistency of the graph structure with the measured data. BMC Systems Biology, 2(84), October 2008.Google Scholar
- Z. M. Saul and V. Filkov. Exploring biological network structure using exponential random graph models. Bioinformatics, 23(19): 2604--2611, 2007. Google ScholarDigital Library
- J. Scott, T. Ideker, R. M. Karp, and R. Sharan. Efficient algorithms for detecting signaling pathways in protein interaction networks. J Comput Biol, 13(2): 133--144, March 2006.Google ScholarCross Ref
- H. Shang, Y. Zhang, X. Lin, and J. X. Yu. Taming verification hardness: an efficient algorithm for testing subgraph isomorphism. PVLDB, 1(1): 364--375, 2008. Google ScholarDigital Library
- Y. Tian, R. C. McEachin, C. Santos, D. J. States, and J. M. Patel. SAGA: a subgraph matching tool for biological graphs. Bioinformatics, 23(2): 232--239, January 2007. Google ScholarDigital Library
- J. R. Ullmann. An algorithm for subgraph isomorphism. Journal of ACM, 23(1): 31--42, 1976. Google ScholarDigital Library
- G. Valiente. Algorithms on Trees and Graphs. Springer-Verlag, Berlin, 2002. Google ScholarDigital Library
- D. W. Williams, J. Huan, and W. Wang. Graph database indexing using structured graph decomposition. pages 976--985, 2007.Google Scholar
- X. Yan, P. S. Yu, and J. Han. Graph indexing: A frequent structure-based approach. In SIGMOD Conference, pages 405--418, 2004. Google ScholarDigital Library
- S. Zhang, M. Hu, and J. Yang. TreePi: A new graph indexing method. In ICDE, pages 966--975, 2007.Google ScholarCross Ref
Index Terms
- Computing subgraph isomorphic queries using structural unification and minimum graph structures
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