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Predecessor Search

  • Reference work entry
  • First Online:
Encyclopedia of Algorithms

  • 194 Accesses

Years and Authors of Summarized Original Work

  • 2006; Pătraşcu, Thorup

Problem Definition

Consider an ordered universe U, and a set \( { T \subset U } \) with \( { |T|=n } \). The goal is to preprocess T, such that the following query can be answered efficiently: given \( { x \in U } \), report the predecessor of x, i.e., \( { \max \{ y \in T \mid y < x \} } \). One can also consider the dynamic problem, where elements are inserted and deleted into T. Let tq be the query time, and tu the update time.

This is a fundamental search problem, with an impressive number of applications. Later, this entry discusses IP lookup (forwarding packets on the Internet), orthogonal range queries and persistent data structures as examples.

The problem was considered in many computational models. In fact, most models below were initially defined to study the predecessor problem.

Comparison model::

The problem can be solved through binary search in \( { \Theta(\lg n) } \)comparisons. There is a lot of...

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Recommended Reading

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Author information

Authors and Affiliations

  1. Computer Science and Artificial Intelligence Laboratory (CSAIL), Massachusetts Institute of Technology (MIT), Cambridge, MA, USA

    Mihai Pătraşcu

Authors
  1. Mihai Pătraşcu
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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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Pătraşcu, M. (2016). Predecessor Search. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2864-4_298

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