, Volume 52, Issue 3, pp 403–411 | Cite as

Optimality in External Memory Hashing



Hash tables on external memory are commonly used for indexing in database management systems. In this paper we present an algorithm that, in an asymptotic sense, achieves the best possible I/O and space complexities. Let B denote the number of records that fit in a block, and let N denote the total number of records. Our hash table uses \(1+O(1/\sqrt{B})\) I/Os, expected, for looking up a record (no matter if it is present or not). To insert, delete or change a record that has just been looked up requires \(1+O(1/\sqrt{B})\) I/Os, amortized expected, including I/Os for reorganizing the hash table when the size of the database changes. The expected external space usage is \(1+O(1/\sqrt{B})\) times the optimum of N/B blocks, and just O(1) blocks of internal memory are needed.


External memory Dictionary Hashing Index 


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  1. 1.
    Aggarwal, A., Vitter, J.S.: The input/output complexity of sorting and related problems. Commun. ACM 31(9), 1116–1127 (1988) CrossRefMathSciNetGoogle Scholar
  2. 2.
    Brodal, G.S., Fagerberg, R.: Lower bounds for external memory dictionaries. In: Proc. 14th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 546–554 (2003) Google Scholar
  3. 3.
    Broder, A.Z., Charikar, M., Frieze, A.M., Mitzenmacher, M.: Min-wise independent permutations. J. Comput. Syst. Sci. 60(3), 630–659 (2000) MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Cesarini, F., Soda, G.: A dynamic hash method with signature. ACM Trans. Database Syst. 16(2), 309–337 (1991) CrossRefGoogle Scholar
  5. 5.
    Gonnet, G.H., Larson, P.-Å.: External hashing with limited internal storage. J. Assoc. Comput. Mach. 35(1), 161–184 (1988) MathSciNetGoogle Scholar
  6. 6.
    Kjellberg, P., Zahle, T.U.: Cascade hashing. In: Dayal, U., Schlageter, G., Lim, H.S. (eds.) Proceedings of 10th International Conference on Very Large Data Bases (VLDB), pp. 481–492. Morgan Kaufmann, Los Altos (1984) Google Scholar
  7. 7.
    Knuth, D.E.: The Art of Computer Programming, vol. 3. Sorting and Searching. Addison-Wesley, Reading (1973) Google Scholar
  8. 8.
    Koushik, M.: Dynamic hashing with distributed overflow space: a file organization with good insertion performance. Inf. Syst. 18(5), 299–318 (1993) CrossRefGoogle Scholar
  9. 9.
    Larson, P.-Å.: Linear hashing with partial expansions. In: Canadian Information Processing Society (ed.) Proceedings of 6th International Conference on Very Large Data Bases (VLDB), pp. 224–232. IEEE Comput. Soc. Press, Silver Spring (1980) Google Scholar
  10. 10.
    Larson, P.-Å.: Linear hashing with overflow-handling by linear probing. ACM Trans. Database Syst. 10(1), 75–89 (1985) CrossRefGoogle Scholar
  11. 11.
    Larson, P.-Å.: Performance analysis of a single-file version of linear hashing. Comput. J. 28(3), 319–329 (1985) CrossRefGoogle Scholar
  12. 12.
    Larson, P.-Å.: Dynamic hash tables. Commun. ACM 31(4), 446–457 (1988) CrossRefMathSciNetGoogle Scholar
  13. 13.
    Litwin, W.: Linear hashing: a new tool for files and tables addressing. In: Proceedings of 6th International Conference on Very Large Data Bases (VLDB), pp. 212–223. IEEE Comput. Soc. Press, Silver Spring (1980) Google Scholar
  14. 14.
    Mullin, J.K.: Tightly controlled linear hashing without separate overflow storage. BIT 21(4), 390–400 (1981) CrossRefGoogle Scholar
  15. 15.
    Ramamohanarao, K., Lloyd, J.W.: Dynamic hashing schemes. Comput. J. 25(4), 479–485 (1982) Google Scholar

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© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.IT University of CopenhagenCopenhagenDenmark

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