Fast and practical algorithms for computing all the runs in a string

  • Authors:

  • Gang Chen;Simon J. Puglisi;W. F. Smyth

  • Affiliations:

  • Department of Computing & Software, McMaster University, Hamilton, Ontario, Canada;Department of Computing, Curtin University, Perth, Australia;Department of Computing & Software, McMaster University, Hamilton, Ontario, Canada and Department of Computing, Curtin University, Perth, Australia

  • Venue:
  • CPM'07 Proceedings of the 18th annual conference on Combinatorial Pattern Matching
  • Year:
  • 2007

Quantified Score

Hi-index 0.00

Visualization

Abstract

A repetition in a string x is a substring w = ue of x, maximum e ≥ 2, where u is not itself a repetition in w. A run in x is a substring w = ueu* of "maximal periodicity", where ue is a repetition and u* a maximum-length possibly empty proper prefix of u. A run may encode as many as |u| repetitions. The maximum number of repetitions in any string x = x[1..n] iswell known to be Θ(n log n). In 2000 Kolpakov & Kucherov showed that the maximum number of runs in x is O(n); they also described a Θ(n)-time algorithm, based on Farach's Θ(n)-time suffix tree construction algorithm (STCA), Θ(n)-time Lempel-Ziv factorization, and Main's Θ(n)-time leftmost runs algorithm, to compute all the runs in x. Recently Abouelhoda et al. proposed a Θ(n)-time Lempel-Ziv factorization algorithm based on an "enhanced" suffix array -- a suffix array together with other supporting data structures. In this paper we introduce a collection of fast space-efficient algorithms for computing all the runs in a string that appear in many circumstances to be superior to those previously proposed.