The analysis of linear probing hashing with buckets

Extended abstract
  • Alfredo Viola
  • Patricio V. Poblete
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1136)


We present the first exact analysis of a linear probing hashing scheme with buckets of size b. From the generating function for the Robin Hood heuristic we obtain exact expressions for the cost of successful searches. For a full table, with the help of Singularity Analysis, we find the asymptotic expansion of this cost up to O((bm)−1). We conclude with a new approach to study certain recurrences that involve truncated exponentials. A new family of numbers that satisfies a recurrence resembling that of the Bernoulli numbers is introduced. These numbers may prove helpful in studying recurrences involving truncated generating functions.


Hash Function Hash Table Average Cost Probability Generate Function Bernoulli Number 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Alfredo Viola
    • 1
  • Patricio V. Poblete
    • 2
  1. 1.Institute de ComputacionUniversidad de la RepúblicaMontevideoUruguay
  2. 2.Department of Computer ScienceUniversity of ChileSantiagoChile

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