Theoretical Computer Science
An on-line string superprimitivity test
Information Processing Letters
Suffix arrays: a new method for on-line string searches
SIAM Journal on Computing
Alphabet dependence in parameterized matching
Information Processing Letters
Multiple matching of parameterized patterns
Theoretical Computer Science
Parameterized pattern matching: algorithms and applications
Journal of Computer and System Sciences
Parameterized pattern matching by Boyer-Moore-type algorithms
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
A New Linear-Time ``On-Line'' Algorithm for Finding the Smallest Initial Palindrome of a String
Journal of the ACM (JACM)
A Space-Economical Suffix Tree Construction Algorithm
Journal of the ACM (JACM)
A fast string searching algorithm
Communications of the ACM
Efficient string matching: an aid to bibliographic search
Communications of the ACM
Faster algorithms for the construction of parameterized suffix trees
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
Finding Maximal Repetitions in a Word in Linear Time
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Border array on bounded alphabet
Journal of Automata, Languages and Combinatorics
Parameterized matching with mismatches
Journal of Discrete Algorithms
Efficient parameterized string matching
Information Processing Letters
Approximate parameterized matching
ACM Transactions on Algorithms (TALG)
Computing Longest Previous Factor in linear time and applications
Information Processing Letters
Periodicity and repetitions in parameterized strings
Discrete Applied Mathematics
Counting suffix arrays and strings
Theoretical Computer Science
Counting Parameterized Border Arrays for a Binary Alphabet
LATA '09 Proceedings of the 3rd International Conference on Language and Automata Theory and Applications
Cover array string reconstruction
CPM'10 Proceedings of the 21st annual conference on Combinatorial pattern matching
Counting and verifying maximal palindromes
SPIRE'10 Proceedings of the 17th international conference on String processing and information retrieval
Reversing longest previous factor tables is hard
WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
Two dimensional parameterized matching
CPM'05 Proceedings of the 16th annual conference on Combinatorial Pattern Matching
Validating the knuth-morris-pratt failure function, fast and online
CSR'10 Proceedings of the 5th international conference on Computer Science: theory and Applications
Validating the Knuth-Morris-Pratt Failure Function, Fast and Online
Theory of Computing Systems
Hi-index | 5.23 |
The parameterized pattern matching problem is to check if there exists a renaming bijection on the alphabet with which a given pattern can be transformed into a substring of a given text. A parameterized border array (p-border array) is a parameterized version of a standard border array, and we can efficiently solve the parameterized pattern matching problem using p-border arrays. In this paper, we present a linear time algorithm to verify if a given integer array is a valid p-border array for a binary alphabet. We also show a linear time algorithm to compute all binary parameterized strings sharing a given p-border array. In addition, we give an algorithm which computes all p-border arrays of length at most n, where n is a given threshold. This algorithm runs in O(B"2^n) time, where B"2^n is the number of all p-border arrays of length n for a binary parameter alphabet. The problems with a larger alphabet are much more difficult. Still, we present an O(n^1^.^5)-time O(n)-space algorithm to verify if a given integer array of length n is a valid p-border array for an unbounded alphabet. The best previously known solution to this task takes time proportional to the n-th Bell number 1e@?"k"="0^~k^nk!, and hence our algorithm is much more efficient. Also, we show that it is possible to enumerate all p-border arrays of length at most n for an unbounded alphabet in O(B^nn^2^.^5) time, where B^n denotes the number of p-border arrays of length n.