Related papers: Quantum Pattern Matching with Wildcards
Let $S_1, S_2 \in \Sigma^*$ strings, we say that $S_1$ {\em jumble match} $S_2$ if they are permutations of each other. Given a text $T$ of size $N$ and a string $S \in \Sigma^*$, the problem of \emph{Jumbled Pattern Matching} (JPM) is to…
The maximum bipartite matching problem is among the most fundamental and well-studied problems in combinatorial optimization. A beautiful and celebrated combinatorial algorithm of Hopcroft and Karp (1973) shows that maximum bipartite…
Quantum computation represents a computational paradigm whose distinctive attributes confer the ability to devise algorithms with asymptotic performance levels significantly superior to those achievable via classical computation. Recent…
In this paper we describe compressed indexes that support pattern matching queries for strings with wildcards. For a constant size alphabet our data structure uses $O(n\log^{\varepsilon}n)$ bits for any $\varepsilon>0$ and reports all…
We propose a probabilistic quantum algorithm that decides whether a monochrome picture matches a given template (or one out of a set of templates). As a major advantage to classical pattern recognition, the algorithm just requires a few…
Quantum computations are typically compiled into a circuit of basic quantum gates. Just like for classical circuits, a quantum compiler should optimize the quantum circuit, e.g. by minimizing the number of required gates. Optimizing quantum…
Permutation patterns and pattern avoidance have been intensively studied in combinatorics and computer science, going back at least to the seminal work of Knuth on stack-sorting (1968). Perhaps the most natural algorithmic question in this…
We study space and time efficient quantum algorithms for two graph problems -- deciding whether an $n$-vertex graph is a forest, and whether it is bipartite. Via a reduction to the s-t connectivity problem, we describe quantum algorithms…
A string matching -- and more generally, sequence matching -- algorithm is presented that has a linear worst-case computing time bound, a low worst-case bound on the number of comparisons (2n), and sublinear average-case behavior that is…
Pattern matching is a fundamental process in almost every scientific domain. The problem involves finding the positions of a given pattern (usually of short length) in a reference stream of data (usually of large length). The matching can…
By means of a simple example it is demonstrated that the task of finding and identifying certain patterns in an otherwise (macroscopically) unstructured picture (data set) can be accomplished efficiently by a quantum computer. Employing the…
We propose fast and practical quantum-inspired classical algorithms for solving linear systems. Specifically, given sampling and query access to a matrix $A\in\mathbb{R}^{m\times n}$ and a vector $b\in\mathbb{R}^m$, we propose classical…
Representing signals with sparse vectors has a wide range of applications that range from image and video coding to shape representation and health monitoring. In many applications with real-time requirements, or that deal with…
Face recognition is one of the most ubiquitous examples of pattern recognition in machine learning, with numerous applications in security, access control, and law enforcement, among many others. Pattern recognition with classical…
Many problems that can be solved in quadratic time have bit-parallel speed-ups with factor $w$, where $w$ is the computer word size. A classic example is computing the edit distance of two strings of length $n$, which can be solved in…
The Longest Common Substring (LCS) and Longest Palindromic Substring (LPS) are classical problems in computer science, representing fundamental challenges in string processing. Both problems can be solved in linear time using a classical…
An efficient quantum algorithm is proposed to solve in polynomial time the parity problem, one of the hardest problems both in conventional quantum computation and in classical computation, on NMR quantum computers. It is based on the…
Longest common substring (LCS), longest palindrome substring (LPS), and Ulam distance (UL) are three fundamental string problems that can be classically solved in near linear time. In this work, we present sublinear time quantum algorithms…
Template matching is widely used for many applications in image and signal processing and usually is time-critical. Traditional methods usually focus on how to reduce the search locations by coarse-to-fine strategy or full search combined…
Two strings are considered to have parameterized matching when there exists a bijection of the parameterized alphabet onto itself such that it transforms one string to another. Parameterized matching has application in software duplication…