TY - JOUR
T1 - Algorithms for anti-powers in strings
AU - Fici, Gabriele
AU - Badkobeh, Golnaz
AU - Puglisi, Simon J.
PY - 2018
Y1 - 2018
N2 - A string S[1,n] is a power (or tandem repeat) of order k and period n/k if it can be decomposed into k consecutive equal-length blocks of letters. Powers and periods are fundamental to string processing, and algorithms for their efficient computation have wide application and are heavily studied. Recently, Fici et al. (Proc. ICALP 2016) defined an anti-power of order k to be a string composed of k pairwise-distinct blocks of the same length (n/k, called anti-period). Anti-powers are a natural converse to powers, and are objects of combinatorial interest in their own right. In this paper we initiate the algorithmic study of anti-powers. Given a string S, we describe an optimal algorithm for locating all substrings of S that are anti-powers of a specified order. The optimality of the algorithm follows form a combinatorial lemma that provides a lower bound on the number of distinct anti-powers of a given order: we prove that a string of length n can contain Θ(n2/k) distinct anti-powers of order k.
AB - A string S[1,n] is a power (or tandem repeat) of order k and period n/k if it can be decomposed into k consecutive equal-length blocks of letters. Powers and periods are fundamental to string processing, and algorithms for their efficient computation have wide application and are heavily studied. Recently, Fici et al. (Proc. ICALP 2016) defined an anti-power of order k to be a string composed of k pairwise-distinct blocks of the same length (n/k, called anti-period). Anti-powers are a natural converse to powers, and are objects of combinatorial interest in their own right. In this paper we initiate the algorithmic study of anti-powers. Given a string S, we describe an optimal algorithm for locating all substrings of S that are anti-powers of a specified order. The optimality of the algorithm follows form a combinatorial lemma that provides a lower bound on the number of distinct anti-powers of a given order: we prove that a string of length n can contain Θ(n2/k) distinct anti-powers of order k.
KW - Algorithms
KW - Anti-powers
KW - Combinatorics on words
KW - Computer Science Applications1707 Computer Vision and Pattern Recognition
KW - Information Systems
KW - Signal Processing
KW - Theoretical Computer Science
KW - Algorithms
KW - Anti-powers
KW - Combinatorics on words
KW - Computer Science Applications1707 Computer Vision and Pattern Recognition
KW - Information Systems
KW - Signal Processing
KW - Theoretical Computer Science
UR - http://hdl.handle.net/10447/336069
M3 - Article
VL - 137
SP - 57
EP - 60
JO - Information Processing Letters
JF - Information Processing Letters
SN - 0020-0190
ER -