Abstract
We introduce the notion of searchability as a property of an in place merging algorithm. It is shown that a pair of sorted arrays can be merged in place in linear time so that a logarithmic time search may be performed at any point during the process. This method is applied to devise an implicit data structure which can support searches in 0(log2 n) time and insertions in 0(log n) time.
This work was supported by NSERC grant A8237.
This work was done while on leave at the University of Waterloo.
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References
Bentley, J.L., D. Detig, L. Guibas and J.B. Saxe: An Optimal Data Structure for Minimal-Storage Dynamic Member Searching, Carnegie-Mellon University, 1978.
Bentley, J.L. and J.B. Saxe: Decomposable Searching Problems I. Static-to-Dynamic Transformation, Journal of Algorithms, 1, 4 (Dec. 1980), 301–358.
Borodin, A.B., L.J. Guibas, N.A. Lynch and A.C. Yao: Efficient Searching Using Partial Ordering, IPL (12,2) April 1981, 71–75.
Eppinger, J.L., An Empirical Study of Insertion and Deletion in Binary Trees (Sept. 1982) unpublished manuscript.
Frederickson, G.N.: Implicit Data Structures with Fast Update, 21st Annual Symposium on Foundations of Computer Science, 1980, 255–259.
Horvath, E.C.: Stable Sorting in Asymptotically Optimal Time and Extra Space, Journal of the ACM, 25, 2 (April 1978), 177–199.
Hwang, F.K. and S. Lin: A Simple Algorithm for Merging Two Disjoint Linearly Ordered Sets, SIAM Journal on Computing, 1, 1 (March 1972), 31–39.
Jonassen, A.T. and D.E. Knuth: A Trivial Algorithm Whose Analysis Isn't, Journal of Computer and System Sciences, 16, 3 (June 1978), 301–322.
Knott, G.D.: Deletion in Binary Storage Trees, Dept. of Computer Science, Stanford University, Rep. STAN-CS-75-491, May 1975.
Knuth, D.E.: The Art of Computer Programming, Vol. 3: Sorting and Searching, Addison-Wesley, Reading, MA., 1973.
Knuth, D.E.: Deletions that Preserve Randomness, IEEE Transactions on Software Engineering, SE-3, 5 (Sept. 1977), 351–359.
Kronrod, M.A.: An Optimal Ordering Algorithm Without a Field of Operation, Dok. Akad. Nauk SSSR, 186 (1969), 1256–1258.
Munro, J.I. and H. Suwanda: Implicit Data Structure for Fast Search and Update, Journal of Computer and System Sciences, 21 2 (Oct. 1980), 236–250.
Trabb Pardo, L.: Stable Sorting and Merging with Optimal Space and Time Bounds, SIAM Journal on Computing, 6, 2 (June 1977), 351–372.
Wong, J.K.: Some Simple In-place merging Algorithms, BIT 21 (1981), 157–166.
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© 1983 Springer-Verlag Berlin Heidelberg
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Munro, J.I., Poblete, P.V. (1983). Searchability in merging and implicit data structures. In: Diaz, J. (eds) Automata, Languages and Programming. ICALP 1983. Lecture Notes in Computer Science, vol 154. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0036934
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DOI: https://doi.org/10.1007/BFb0036934
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