A Work-Time Optimal Algorithm for Computing All String Covers

  title={A Work-Time Optimal Algorithm for Computing All String Covers},
  author={Costas S. Iliopoulos and Kunsoo Park},
  journal={Theor. Comput. Sci.},
Enhanced string covering
New and Efficient Approaches to the Quasiperiodic Characterisation of a String
New, simple, easily-computed, and widely applicable notions of string covering that provide an intuitive and useful characterisation of a string and its prefixes are proposed: the enhanced cover and theEnhanced cover array.
Computing the lambda-covers of a string
Computing the k-covers of a string
This work generalizes the k-Cover Problem, whereby a set of k substrings of different lengths are considered, which can be computed using the general algorithm in OðnÞ time for constant alphabet size.
On left and right seeds of a string
Algorithms for Computing the λ-regularities in Strings
A general algorithm is presented for computing all the λ-combinations of a given string, since they serve as candidates for both δ-covers and ε-seeds, which is O(n$^2$) time.
Generalized approximate regularities in strings
This work focuses on generalized string regularities and study the minimum approximate λ-cover problem and the minimum approximations of a string under a variety of distance models containing the Hamming distance, the edit distance and the weighted edit distance.
Computing the λ-Seeds of a String
An efficient algorithm is presented that can compute all the λ-seeds of x in O(n) time and find all the sets of λ substrings of x that cover a superstring of x.
Computing the lambda-Seeds of a String
An efficient algorithm is presented that can compute all the λ-seeds of x in O(n2) time and find all the sets of λ substrings of x that cover a superstring of x.
Quasiperiodicities in Fibonacci strings
This paper identifies all covers, left/right seeds and seeds of a Fibonacci string and all covers of a circular Fib onacci string.


Work-Time Optimal Parallel Prefix Matching (Extended Abstract)
This work presents a parallel algorithm for the prefix matching problem over general alphabets whose text search takes optimal O(α(m)) time and preprocessing takes optimalO(log log m) time, where α(m) is the inverse Ackermann function.
Optimal Parallel Algorithms for Periods, Palindromes and Squares (Extended Abstract)
The lower bounds for testing if a string is square-free and finding all initial palindromes are derived by a modification of a lower bound for finding the period of a string.
Covering a String
AnO(n logn)-time algorithm for finding all the seeds of a given string of lengthn is presented and the concept of repetitiveness is generalized as follows.
Computing the covers of a string in linear time
The characterization theorem gives rise to a simple recursive algorithm which computes all the covers of x in time \Theta(n) by avoiding unnecessary checks, and appears to execute more quickly than that given in [2].
The Parallel Simplicity of Compaction and Chaining
  • P. Ragde
  • Computer Science, Mathematics
    J. Algorithms
  • 1993
The ordered chaining problem is shown to be solvable in time O(α(k)) with n processors (where α is a functional inverse of Ackermann's function) and unordered chaining can be solved in constant time with nprocessor when k.
Covering a Circular String with Substrings of Fixed Length
This paper considers the problem of determining the minimum cardinality of a set Uk which guarantees that every circular string C(x) of length n≥k can be covered and shows how, for any positive integer m, to choose the elements of Uk so that, for sufficiently large k, uk–m, where uk=|Uk| and σ is the size of the alphabet on which the strings are defined.
The subtree max gap problem with application to parallel string covering
The algorithm for the subtree max gap problem follows a series of reductions to other combinatorial problems which are interesting on their own merit, and runs in O(log n) time using n processors on the concurrent-read exclusive-write parallel random access machine.
Optimal Doubly Logarithmic Parallel Algorithms Based on Finding All Nearest Smaller Values
An O (log log n ) time optimal parallel algorithm is given for the all nearest smaller values problem and it is shown that any optimal CRCW PRAM algorithm for the triangulation problem requires Ω( log log n) time.
Testing String Superprimitivity in Parallel
Optimal Superprimitivity Testing for Strings