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Predecessor Search, String Algorithms and Data Structures

  • Reference work entry
  • First Online:
Encyclopedia of Algorithms

  • 137 Accesses

Years and Authors of Summarized Original Work

  • 1975; Van Emde Boas

  • 1993; Fredman, Willard

  • 2002; Beame, Fich

  • 2006; PÇŽtraÅŸcu, Thorup

  • 2007; Andersson, Thorup

  • 2014; PÇŽtraÅŸcu, Thorup

Problem Definition

Given a set S of n keys from the set [1…2ℓ], the goal of predecessor search is to return, given a key y ∈ [1…2ℓ], the largest key x ∈ S such that x ≤ y. We have the following models:

Comparison model

Balanced binary search trees [1, 6] can solve the problem in optimal O(logn) time in the comparison model, in which the key can only be manipulated through comparisons with each other.

External memory model

In this model, it is assumed that the data is read and written into blocks of B elements (integers in our case) and the cost of a query or algorithm is the number of read or written blocks. In this model, B-trees [7] can solve the problem in O(log B n) time and O(n) space.

RAM model

This is the main subject of study. The model assumes that all standard arithmetic and logic operations (including...

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Recommended Reading

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Author information

Authors and Affiliations

  1. Department of Computer Science, Helsinki Institute for Information Technology (HIIT), University of Helsinki, Helsinki, Finland

    Djamal Belazzougui

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  1. Djamal Belazzougui
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Correspondence to Djamal Belazzougui .

Editor information

Editors and Affiliations

  1. Department of Electrical Engineering and Computer Science, Northwestern University, Evanston, IL, USA

    Ming-Yang Kao

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Belazzougui, D. (2016). Predecessor Search, String Algorithms and Data Structures. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2864-4_632

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