The “runs” conjecture

Authors:
Maxime Crochemore;Lucian Ilie;Liviu Tinta
Affiliations:
Department of Computer Science, Kings College London, London WC2R 2LS, UK and Université Paris-Est, France;Department of Computer Science, University of Western Ontario, N6A 5B7, London, Ontario, Canada;Department of Computer Science, University of Western Ontario, N6A 5B7, London, Ontario, Canada
Venue:
Theoretical Computer Science
Year:
2011

Citing 12
Cited 5

An O(n log n) algorithm for finding all repetitions in a string

Journal of Algorithms
Transducers and repetitions

Theoretical Computer Science
Detecting leftmost maximal periodicities

Discrete Applied Mathematics - Combinatorics and complexity
Finding Maximal Repetitions in a Word in Linear Time

FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
The number of runs in a string

Information and Computation
Computing Longest Previous Factor in linear time and applications

Information Processing Letters
Maximal repetitions in strings

Journal of Computer and System Sciences
How many runs can a string contain?

Theoretical Computer Science
Towards a Solution to the "Runs" Conjecture

CPM '08 Proceedings of the 19th annual symposium on Combinatorial Pattern Matching
Not So Many Runs in Strings

Language and Automata Theory and Applications
Repetitions in strings: Algorithms and combinatorics

Theoretical Computer Science
The number of runs in a string: improved analysis of the linear upper bound

STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science

Hunting redundancies in strings

DLT'11 Proceedings of the 15th international conference on Developments in language theory
Computing the maximal-exponent repeats of an overlap-free string in linear time

SPIRE'12 Proceedings of the 19th international conference on String Processing and Information Retrieval
Computing maximum number of runs in strings

SPIRE'12 Proceedings of the 19th international conference on String Processing and Information Retrieval
The total run length of a word

Theoretical Computer Science
Extracting powers and periods in a word from its runs structure

Theoretical Computer Science

Quantified Score

Hi-index	5.23

Visualization

Abstract

The ''runs'' conjecture, proposed by Kolpakov and Kucherov (1999) [7], states that the number of occurrences of maximal repetitions (runs) in a string of length n, runs(n), is at most n. We almost solve the conjecture by proving that runs(n)=