Related papers: A Note on Efficient Computation of All Abelian Per…

Abelian periodicity of strings has been studied extensively over the last years. In 2006 Constantinescu and Ilie defined the abelian period of a string and several algorithms for the computation of all abelian periods of a string were…

Constantinescu and Ilie (Bulletin of the EATCS 89, 167-170, 2006) introduced the idea of an Abelian period with head and tail of a finite word. An Abelian period is called full if both the head and the tail are empty. We present a simple…

The abelian pattern matching problem consists in finding all substrings of a text which are permutations of a given pattern. This problem finds application in many areas and can be solved in linear time by a naive sliding window approach.…

Two strings x and y are said to be Abelian equivalent if x is a permutation of y, or vice versa. If a string z satisfies z = xy with x and y being Abelian equivalent, then z is said to be an Abelian square. If a string w can be factorized…

Abelian string matching problems are becoming an object of considerable interest in last years. Very recently, Alatabbi et al. \cite{AILR2015} presented the first solution for the longest common Abelian factor problem for a pair of strings,…

In a recent work I developed a formula for efficiently calculating the number of abelian squares of length $t+t$ over an alphabet of size $d$, where $d$ may be very large. Here I show how the expressiveness of a certain class of…

In this paper we consider the problem of computing the longest common abelian factor (LCAF) between two given strings. We present a simple $O(\sigma~ n^2)$ time algorithm, where $n$ is the length of the strings and $\sigma$ is the alphabet…

We prove 3SUM-hardness (no strongly subquadratic-time algorithm, assuming the 3SUM conjecture) of several problems related to finding Abelian square and additive square factors in a string. In particular, we conclude conditional optimality…

Constantinescu and Ilie (Bulletin EATCS 89, 167--170, 2006) introduced the notion of an \emph{Abelian period} of a word. A word of length $n$ over an alphabet of size $\sigma$ can have $\Theta(n^{2})$ distinct Abelian periods. The…

Given a string on an integer alphabet, we present an algorithm that computes the set of all distinct squares belonging to this string in time linear to the string length. As an application, we show how to compute the tree topology of the…

We propose efficient algorithms for enumerating maximal common subsequences (MCSs) of two strings. Efficiency of the algorithms are estimated by the preprocessing-time, space, and delay-time complexities. One algorithm prepares a…

In this paper we show that certain special cases of the hidden subgroup problem can be solved in polynomial time by a quantum algorithm. These special cases involve finding hidden normal subgroups of solvable groups and permutation groups,…

I present a recursive formula for calculating the number of abelian squares of length $n+n$ over an alphabet of size $d$. The presented formula is similar to a previously known formula but has substantially lower complexity when $d\gg n$.

Suppose we want to seek the longest common subsequences (LCSs) of two strings as informative patterns that explain the relationship between the strings. The dynamic programming algorithm gives us a table from which all LCSs can be extracted…

We consider the Abelian longest common factor problem in two scenarios: when input strings are uncompressed and are of size $n$, and when the input strings are run-length encoded and their compressed representations have size at most $m$.…

It is believed that there is no efficient classical algorithm to determine the linear structure of Boolean function. We investigate an extension of Simon's period-finding quantum algorithm, and propose an efficient quantum algorithm to…

The hidden subgroup problem~(HSP) is one of the most important problems in quantum computation. Many problems for which quantum algorithm achieves exponential speedup over its classical counterparts can be reduced to the Abelian HSP.…

This paper describes a quantum algorithm for efficiently decomposing finite Abelian groups. Such a decomposition is needed in order to apply the Abelian hidden subgroup algorithm. Such a decomposition (assuming the Generalized Riemann…

Dating to 1994, Simon's period-finding algorithm is among the earliest and most fragile of quantum algorithms. The algorithm's fragility arises from the requirement that, to solve an n qubit problem, one must fault-tolerantly sample O(n)…

We first prove a one-to-one correspondence between finding Hamiltonian cycles in a cubic planar graphs and finding trees with specific properties in dual graphs. Using this information, we construct an exact algorithm for finding…