On the structure of run-maximal strings

Authors:
Andrew Baker;Antoine Deza;Frantisek Franek
Affiliations:
Advanced Optimization Laboratory, Department of Computing and Software, McMaster University, Hamilton, Ontario, Canada;Advanced Optimization Laboratory, Department of Computing and Software, McMaster University, Hamilton, Ontario, Canada;Advanced Optimization Laboratory, Department of Computing and Software, McMaster University, Hamilton, Ontario, Canada
Venue:
Journal of Discrete Algorithms
Year:
2012

Citing 8
Cited 2

Detecting leftmost maximal periodicities

Discrete Applied Mathematics - Combinatorics and complexity
Repetitive perhaps, but certainly not boring

Theoretical Computer Science
Finding Maximal Repetitions in a Word in Linear Time

FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
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
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

A computational framework for determining run-maximal strings

Journal of Discrete Algorithms
A d-step approach to the maximum number of distinct squares and runs in strings

Discrete Applied Mathematics

Quantified Score

Hi-index	0.00

Visualization

Abstract

We present a combinatorial structure consisting of a special cover of a string by squares. We characterize the covering property of run-maximal strings, i.e. strings achieving the maximal number of runs. The covering property leads to a compression scheme which is particularly efficient for run-maximal strings. It also yields a significant speed improvement in the computer search for good run-maximal string candidates. The implementation of the search and preliminary computational results are discussed.