Related papers: Quantum Algorithms for String Processing
Constraint programming (CP) is a paradigm used to model and solve constraint satisfaction and combinatorial optimization problems. In CP, problems are modeled with constraints that describe acceptable solutions and solved with backtracking…
Quantum algorithm, as compared to classical algorithm, plays a notable role in solving linear systems of equations with an exponential speedup. Here, we demonstrate a method for solving a particular system of equations by using the concept…
We study some extensions of Grover's quantum searching algorithm. First, we generalize the Grover iteration in the light of a concept called amplitude amplification. Then, we show that the quadratic speedup obtained by the quantum searching…
In this paper we consider several variants of the pattern matching problem. In particular, we investigate the following problems: 1) Pattern matching with k mismatches; 2) Approximate counting of mismatches; and 3) Pattern matching with…
Quantum computers use the quantum interference of different computational paths to enhance correct outcomes and suppress erroneous outcomes of computations. In effect, they follow the same logical paradigm as (multi-particle)…
We demonstrate the implementation of a quantum algorithm for estimating the number of matching items in a search operation using a two qubit nuclear magnetic resonance (NMR) quantum computer.
Search is one of the most commonly used primitives in quantum algorithm design. It is known that quadratic speedups provided by Grover's algorithm are optimal, and no faster quantum algorithms for Search exist. While it is known that at…
Quantum sampling, a fundamental subroutine in numerous quantum algorithms, involves encoding a given probability distribution in the amplitudes of a pure state. Given the hefty cost of large-scale quantum storage, we initiate the study of…
We study 4 problems in string matching, namely, regular expression matching, approximate regular expression matching, string edit distance, and subsequence indexing, on a standard word RAM model of computation that allows logarithmic-sized…
We present a quantum algorithm for finding the minimum of a function based on multistep quantum computation and apply it for optimization problems with continuous variables, in which the variables of the problem are discretized to form the…
In this paper, we revisit the much studied problem of Pattern Matching with Swaps (Swap Matching problem, for short). We first present a graph-theoretic model, which opens a new and so far unexplored avenue to solve the problem. Then, using…
We put forth a new string matching algorithm which matches the pattern from neither the left nor the right end, instead a special position. Comparing with the Knuth-Morris-Pratt algorithm and the Boyer-Moore algorithm, the new algorithm is…
Searching for all occurrences of a pattern in a text is a fundamental problem in computer science with applications in many other fields, like natural language processing, information retrieval and computational biology. In the last two…
We introduce a new string matching problem called order-preserving matching on numeric strings where a pattern matches a text if the text contains a substring whose relative orders coincide with those of the pattern. Order-preserving…
A quantum algorithm for general combinatorial search that uses the underlying structure of the search space to increase the probability of finding a solution is presented. This algorithm shows how coherent quantum systems can be matched to…
In this paper we revisit the classical regular expression matching problem, namely, given a regular expression $R$ and a string $Q$, decide if $Q$ matches one of the strings specified by $R$. Let $m$ and $n$ be the length of $R$ and $Q$,…
We study the fundamental problem of finding the best string to represent a given set, in the form of the Closest String problem: Given a set $X \subseteq \Sigma^d$ of $n$ strings, find the string $x^*$ minimizing the radius of the smallest…
Many important computer science problems can be reduced to clause satisfaction problem. We are given $n$ Boolean variables $x_{k}$ and $m$ clauses $c_{j}$ where each clause is a function of values of some of the variables. We want to find…
The Maximum Matching problem has a quantum query complexity lower bound of $\Omega(n^{3/2})$ for graphs on $n$ vertices represented by an adjacency matrix. The current best quantum algorithm has the query complexity $O(n^{7/4})$, which is…
Multiple string matching is known as locating all the occurrences of a given number of patterns in an arbitrary string. It is used in bio-computing applications where the algorithms are commonly used for retrieval of information such as…