In this paper we consider the problem of using disk blocks efficiently in searching graphs that are too large to fit in internal memory. Our model allows a vertex to be represented any number of times on the disk in order to take advantage of redundancy. We give matching upper and lower bounds for completed-ary trees andd-dimensional grid graphs, as well as for classes of general graphs that intuitively speaking have a close to uniform number of neighbors around each vertex. We also show that, for the special case of grid graphs blocked with isothetic hypercubes, there is a provably better speed-up if even a small amount of redundancy is permitted.
Key wordsExternal searching Isothetic hypercubes Blocking Input/output complexity Redundancy
Unable to display preview. Download preview PDF.
- D. E. Knuth,The Art of Computer Programming, Vol. 3, Addison-Wesley, Reading, MA, 1973.Google Scholar
- A. Aggarawal and J. Park, Notes on Searching in Multidimensional Monotone Arrays,Proceedings of the 29th Annual IEEE Symposium on Foundations of Computer Science, White Plains, NY, October 1988, pp. 497–512.Google Scholar
- J. D. Ullman,Principles of Database and Knowledge-Base Systems, Computer Science Press, Rockville, MD, 1988.Google Scholar
- A. Borodin, S. Irani, P. Raghavan, and B. Schieber, Competitive Paging with Locality of Reference,Proceedings of the 23rd ACM Symposium on Theory of Computing, New Orleans, LA, May 1991, pp. 249–259.Google Scholar
- A. L. Rosenberg, Encoding Data Structures in Trees,J. Assoc. Comput. Mach. 26 (1979), 668–689.Google Scholar
- F. R. K. Chung, A. L. Rosenberg, and L. Snyder, Perfect Storage Representations for Families of Data Structures,SIAM J. Algebraic Discrete Methods 4 (1983), 548–565.Google Scholar
- R. Aleliunas and A. L. Rosenberg, On Embedding Rectangular Grids in Square Grids,IEEE Trans. Comput. 31 (1982), 907–913.Google Scholar
- R. J. Lipton, S. C. Eisenstat, and R. A. DeMillo, Space and Time Hierarchies for Classes of Control Structures and Data Structures,J. Assoc. Comput. Mach. 23 (1976), 720–732.Google Scholar
- C. Berge,Graphs and Hypergraphs, 2nd edn., North-Holland, Amsterdam, 1976.Google Scholar
- G. Reich and P. Widmayer, Beyond Steiner's Problem: A VSLI Oriented Generalization, inGraph-Theoretic Concepts in Computer Science: Proceedings of the 15th International Workshop WG '89 (G. Goos and J. Hartmanis, eds.), Lecture Notes in Computer Science, Vol. 411, Springer-Verlag, Berlin, 1990, pp. 196–210.Google Scholar
- E. Ihler, Bounds on the Quality of Approximate Solutions to the Group Steiner Problem, inGraph-Theoretic Concepts in Computer Science, Proceedings of the 16th International Workshop WG '90 (G. Goos and J. Hartmanis, eds.), Lecture Notes in Computer Science, Vol. 484, Springer-Verlag, Berlin, 1991, pp. 109–118.Google Scholar
- M. R. Garey and D. S. Johnson,Computers and Intractability: A Guide to the Theory of NP-Completeness, Freeman, San Francisco, CA, 1979.Google Scholar