The Community for Technology Leaders
RSS Icon
Subscribe
Issue No.10 - Oct. (2013 vol.25)
pp: 2245-2256
Jianguo Wang , The Hong Kong Polytechnic University, Hong Kong
Eric Lo , The Hong Kong Polytechnic University, Hong Kong
Man Lung Yiu , The Hong Kong Polytechnic University, Hong Kong
ABSTRACT
A graph is called hidden if the edges are not explicitly given and edge probe tests are required to detect the presence of edges. This paper studies the $(k)$ most connected vertices ($(k)$MCV) problem on hidden bipartite graphs, which has applications in spatial databases, graph databases, and bioinformatics. There is a prior work on the $(k)$MCV problem, which is based on the "2-vertex testing" model, i.e., an edge probe test can only reveal the existence of an edge between two individual vertices. We study the $(k)$MCV problem, in the context of a more general edge probe test model called "group testing." A group test can reveal whether there exists some edge between a vertex and a group of vertices. If group testing is used properly, a single invocation of a group test can reveal as much information as multiple invocations of 2-vertex tests. We discuss the cases and applications where group testing could be used, and present an algorithm, namely, GMCV, that adaptively leverages group testing to solve the $(k)$MCV problem.
INDEX TERMS
Testing, Probes, Image edge detection, Bipartite graph, Proteins, Bioinformatics, Switches, Query processing, Testing, Probes, Image edge detection, Bipartite graph, Proteins, Bioinformatics, Switches, graphs and networks
CITATION
Jianguo Wang, Eric Lo, Man Lung Yiu, "Identifying the Most Connected Vertices in Hidden Bipartite Graphs Using Group Testing", IEEE Transactions on Knowledge & Data Engineering, vol.25, no. 10, pp. 2245-2256, Oct. 2013, doi:10.1109/TKDE.2012.178
REFERENCES
[1] L.A. Adamic and B.A. Huberman, "Power-Law Distribution of the World Wide Web," Science, vol. 287, pp. 2115, 2000.
[2] R. Albert, H. Jeong, and A.L. Barabasi, "The Diameter of the World Wide Web," Nature, vol. 401, pp. 130-131, 1999.
[3] N. Alon and V. Asodi, "Learning a Hidden Subgraph," SIAM J. Discrete Math., vol. 18, pp. 697-712, 2005.
[4] N. Alon, R. Beigel, S. Kasif, S. Rudich, and B. Sudakov, "Learning a Hidden Matching," SIAM J. Computing, vol. 33, pp. 487-501, 2004.
[5] D. Angluin and J. Chen, "Learning a Hidden Graph Using O(log n) Queries per Edge," J. Computer and System Sciences, vol. 74, pp. 546-556, 2008.
[6] A. Bar-Noy, F.K. Hwang, I. Kessler, and S. Kutten, "A New Competitive Algorithm for Group Testing," Discrete Applied Math., vol. 52, no. 1, pp. 29-38, 1994.
[7] M. Bouvel, V. Grebinski, and G. Kucherov, "Combinatorial Search on Graphs Motivated by Bioinformatics Applications: A Brief Survey," Proc. Int'l Workshop Graph-Theoretic Concepts in Computer Science, pp. 16-27, 2005.
[8] C. Chen, X. Yan, P.S. Yu, J. Han, D.-Q. Zhang, and X. Gu, "Towards Graph Containment Search and Indexing," Proc. Int'l Conf. Very Large Data Bases (VLDB), pp. 926-937, 2007.
[9] J. Cheng, Y. Ke, W. Ng, and A. Lu, "Fg-index: Towards Verification-Free Query Processing on Graph Databases," Proc. ACM SIGMOD Int'l Conf. Management of Data, pp. 857-872, 2007.
[10] E.D. Demaine, A. López-Ortiz, and J.I. Munro, "Adaptive Set Intersections, Unions, and Differences," Proc. Ann. ACM-SIAM Symp. Discrete Algorithms (SODA), pp. 743-752, 2000.
[11] R. Dorfman, "The Detection of Defective Members of Large Populations," Annals of Math. Statistics, vol. 14, pp. 436-440, 1943.
[12] D. Du and F. Hwang, Combinatorial Group Testing and Its Applications. World Scientific Press, 2000.
[13] D. Eppstein, M.T. Goodrich, and D.S. Hirschberg, "Improved Combinatorial Group Testing Algorithms for Real-World Problem Sizes," SIAM J. Computing, vol. 36, pp. 1360-1375, 2006.
[14] R. Fagin, A. Lotem, and M. Naor, "Optimal Aggregation Algorithms for Middleware," Proc. ACM Symp. Principles of Database Systems (PODS), pp. 102-113, 2001.
[15] W.I. Gasarch and C.H. Smith, "Learning via Queries," J. ACM, vol. 39, pp. 649-674, 1992.
[16] O. Goldreich, S. Goldwasser, and D. Ron, "Property Testing and Its Connection to Learning and Approximation," J. ACM, vol. 45, pp. 653-750, 1998.
[17] E. Golemis and P. Adams, Protein-Protein Interactions: A Molecular Cloning Manual. Cold Spring Harbor Laboratory Press, 2005.
[18] V. Grebinski and G. Kucherov, "Reconstructing a Hamiltonian Cycle by Querying the Graph: Application to DNA Physical Mapping," Discrete Applied Math., vol. 88, pp. 147-165, 1998.
[19] H. Hu, D.L. Lee, and V.C.S. Lee, "Distance Indexing on Road Networks," Proc. Int'l Conf. Very Large Data Bases (VLDB), pp. 894-905, 2006.
[20] I.F. Ilyas, G. Beskales, and M.A. Soliman, "A Survey of Top-k Query Processing Techniques in Relational Database Systems," ACM Computing Surveys, vol. 40, no. 4, pp. 1-58, 2008.
[21] N.T.-M. Laurent, L. Trilling, and J. louis Roch, A Novel Pooling Design for Protein-Protein Interaction Mapping, 2004.
[22] Y. Li, M.T. Thai, Z. Liu, and W. Wu, "Protein-Protein Interaction and Group Testing in Bipartite Graphs," Int'l J. Bioinformatics Research and Applications, vol. 1, pp. 414-419, 2005.
[23] A. Parameswaran, A.D. Sarma, H. Garcia-Molina, N. Polyzotis, and J. Widom, "Human-Assisted Graph Search: It's Okay to Ask Questions," Proc. VLDB Endowment, vol. 4, no. 5, pp. 267-278, 2011.
[24] P. Raghavan and C.D. Tompson, "Randomized Rounding: A Technique for Provably Good Algorithms and Algorithmic Proofs," Combinatorica, vol. 7, no. 4, pp. 365-374, 1987.
[25] H. Samet, J. Sankaranarayanan, and H. Alborzi, "Scalable Network Distance Browsing in Spatial Databases," Proc. ACM SIGMOD Int'l Conf. Management of Data, pp. 43-54, 2008.
[26] J. Schlaghoff and E. Triesch, "Improved Results for Competitive Group Testing," Combinatorics, Probability and Computing, vol. 14, pp. 191-202, 2005.
[27] H. Shang, Y. Zhang, X. Lin, and J.X. Yu, "Taming Verification Hardness: An Efficient Algorithm for Testing Subgraph Isomorphism," Proc. VLDB Endowment, vol. 1, pp. 364-375, 2008.
[28] C. Sheng, Y. Tao, and J. Li, "Exact and Approximate Algorithms for the Most Connected Vertex Problem," ACM Trans. Database Systems, vol. 37, no. 2, pp. 1-39, 2012.
[29] Y. Tao, C. Sheng, and J. Li, "Finding Maximum Degrees in Hidden Bipartite Graphs," Proc. ACM SIGMOD Int'l Conf. Management of Data, pp. 891-902, 2010.
[30] J.R. Thomsen, M.L. Yiu, and C.S. Jensen, "Effective Caching of Shortest Paths for Location-Based Services," Proc. ACM SIGMOD Int'l Conf. Management of Data, pp. 313-324, 2012.
[31] F. Wei, "TEDI: Efficient Shortest Path Query Answering on Graphs," Proc. ACM SIGMOD Int'l Conf. Management of Data, pp. 99-110, 2010.
[32] Y. Xuan, I. Shin, M. Thai, and T. Znati, "Detecting Application Denial-of-Service Attacks: A Group-Testing-Based Approach," IEEE Trans. Parallel and Distributed Systems, vol. 21, no. 8, pp. 1203-1216, Aug. 2010.
[33] S. Zhang, J. Li, H. Gao, and Z. Zou, "A Novel Approach for Efficient Supergraph Query Processing on Graph Databases," Proc. Int'l Conf. Extending Database Technology (EDBT), pp. 204-215, 2009.
71 ms
(Ver 2.0)

Marketing Automation Platform Marketing Automation Tool