This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
Algorithms for Searching Massive Graphs
April 1994 (vol. 6 no. 2)
pp. 225-238

Given a large graph, stored on disk, there is often a need to perform a search over this graph. Such a need could arise, for example, in the search component of a data-intensive expert system or to solve path problems in deductive database systems. In this paper, we present a novel data structuring technique and show how a branch-and-bound search algorithm can use this data structuring to prune the search space. Simulation results confirm that, using these techniques, a search can be expedited significantly without incurring a large storage penalty. As a side benefit, it is possible to organize the search to obtain successive approximations to the desired solution with considerable reduction in the total search.

[1] R. Agrawal, "Alpha: An Extension of Relational Algebra to Express a Class of Recursive Queries,"Proc. Third Int'l Conf. Data Eng., CS Press, Los Alamitos, Calif., Order No. FN762, 1987, pp. 580-590.
[2] R. Agrawalet al., "Efficient management of transitive relationships in large data and knowledge bases," in [42], pp. 253-262, 1989.
[3] R. Agarwal and H. V. Jagadish, "Materialization and incremental updata of path information," inProc. IEEE 5th Int. Conf. Data Engineering, Los Angeles, Feb. 1989, pp. 374-383.
[4] R. Agarwal and H. V. Jagadish, "Hybrid transitive closure algorithms," inProc. 16th Int. Conf. Very Large Data Bases, Brisbane, Australia, Aug. 1990, pp. 326-334.
[5] R. Agrawal and H. V. Jagadish, "Direct algorithms for computing the transitive closure of database relations," inProc. 13th Int. Conf. Very Large Data Bases, Brighton, England, Sept. 1987, pp. 255-266.
[6] F. Bancilhon, "Naive evaluation of recursively defined relations," Tech. Rep. DB-004-85, MCC, Austin, TX, 1985.
[7] A. Barr and E. A. Feigenbaum,The Handbook of Artificial Intelligence, vol. I, Los Altos, CA: William Kaufmann, 1981.
[8] J. Biskup, U. Raesch, and H. Stiefeling, "An extended relational query language for knowledgebase support," Institut fuer Informatik, Hildesheim, Germany, 1987.
[9] J. Blakeley, P. Larson, and F. Tompa, "Efficiently updating materialized views," inProc. ACM-SIGMOD Int. Conf Management of Data, Washington, May 28-30, 1986.
[10] B. Carre,Graphs and Networks. Oxford: Clarendon, 1978.
[11] I. F. Cruz and T. S. Norvell, "Aggregative closure: An extension of transitive closure," inProc. IEEE 5th Int. Conf. Data Engineering, Los Angeles, CA, Feb. 1989.
[12] U. Dayal and J. M. Smith, "PROBE: A knowledge-oriented data-base management system," inProc. Islamorada Workshop Large Scale Knowledge Base and Reasoning Systems, Islamorada, FL, Feb. 1985, pp. 103-137.
[13] E. W. Dijkstra, "A note on two problems in connections with graphs."Numer. Math., vol. 1, pp. 269-271, 1959.
[14] S. E. Dreyfus, "An appraisal of some shortest path algorithms,"Operations Res., vol. 17, no. 3, pp. 395-412, 1968.
[15] G. Gardarin, E. Simon, and L. Verlaine, "Querying real time relational data bases," inProc. IEEE-ICC Int. Conf., Amesterdam, May 1984, pp. 757-761.
[16] M. R. Garey and D. S. Johnson,Computers and Intractability: A Guide to Theory of NP-Completeness. San Francisco, CA: Freeman, 1979.
[17] A. Guttman, "New features for relational database systems to support CAD applications," Ph.D. dissert., Comput. Sci. Dept., Univ. California, Berkley, June 1984.
[18] E. Hanson, "A performance analysis of view materialization strategies,"ACM-SIGMOD Int. Conf. Management of Data, San Francisco, CA, May 28-30, 1987.
[19] P. E. Hart, N. Nilsson, B. Raphael, "A formal basis for the heuristic determination of minimum cost paths,"IEEE Trans. Syst. Science and Cybern., vol. SSC-4, no. 2, pp. 100-107, 1968.
[20] Y. E. Ioannidis, "On the computation of the transitive closure of relational operators, " inProc. 12th Int. Conf. Very Large Databases, Kyoto, Japan, 1986.
[21] H. V. Jagadish, "A compression technique to materialize transitive closure,"ACM Trans. Database Syst., vol. 14, no. 4, Dec. 1990. (Previously appred as "A compressed transitive closure technique for efficient fixed-point query processing," inProc. 2nd Int. Conf. Expert Database Systems, Tyson's Corner, VA, 1988).
[22] M. Jarke and J. Schmidt, "Query processing strategies in the Pascal/ R relational database management system," inProc. ACM-SIGMOD Int. Conf. Management of Data, Orlando, FL, June 1982, pp. 215- 224.
[23] R. Kung, E. Hanson, Y. Ioannidis, T. Sellis, L. Shapiro, and M. Stonebraker, "Heuristic search in data base systems," inProc. 1st Int. Workshop Expert Data Base Systems, Kiawah Island, SC, Oct. 1984.
[24] T. H. Merrett,Relational Information System. Reston, VA: Reston Publishing, 1984.
[25] C. H. Papadimitriou and K. Steiglitz,Combinatorial Optimization: Algorithms and Complexity. Englewood Cliffs, NJ: Prentice-Hall, 1982.
[26] J. Pearl and B. Raphael, "A formal basis for the heuristic determination of minimum cost paths,"IEEE Trans. Systems Science Cybern., vol. 4, no. 2, pp. 100-107, 1968.
[27] A. Rosenthal, S. Heiler, U. Dayal, and F. Manola, "Traversal recursion: A practical approach to supporting recursive applications," inProc. IEEE 3rd Int. Conf. Data Engineering, Los Angeles, Feb. 1987, pp. 580-590 Also inIEEE Trans. Software Eng.vol. 14, no. 7, 879-885, July 1988.
[28] J. Blakeley, P. Larson, and F. Tompa, "Efficiently updating materialized views," inProc. ACM-SIGMOD Int. Conf Management of Data, Washington, May 28-30, 1986.
[29] S. Sippu and E. Soisalon-Soininen, "Aggregative closure: An extension of transitive closure," inProc. IEEE 5th Int. Conf. Data Engineering, Los Angeles, Feb, 1989.
[30] P. Valduriez and H. Boral, "Evaluation of recursive queries using join indices," inProc. 12th Int. Conf. Very Large Data Bases, vol. 12, no. 2, Aug. 1986, pp. 403-411.
[31] P. Valduriez and H. Boral, "Evaluation of recursive queries using join indices," inProc. 12th Int. Conf. Very Large Data Bases, Kyoto, Japan, Aug. 1986, pp. 403-411.

Index Terms:
graph theory; search problems; deductive databases; data structures; query processing; very large databases; approximation theory; database theory; massive graphs; simulation; disk storage; data-intensive expert system; path problems; deductive database systems; data structuring technique; branch and bound search algorithm; search space pruning; successive approximations; path queries; query processing; shortest distance
Citation:
R. Agrawal, H.V. Jagadish, "Algorithms for Searching Massive Graphs," IEEE Transactions on Knowledge and Data Engineering, vol. 6, no. 2, pp. 225-238, April 1994, doi:10.1109/69.277767
Usage of this product signifies your acceptance of the Terms of Use.