Related papers: On the Average-case Complexity of Pattern Matching…
Graph matching is a fundamental problem in pattern recognition, with many applications such as software analysis and computational biology. One well-known type of graph matching problem is graph isomorphism, which consists of deciding if…
In dictionary learning, also known as sparse coding, the algorithm is given samples of the form $y = Ax$ where $x\in \mathbb{R}^m$ is an unknown random sparse vector and $A$ is an unknown dictionary matrix in $\mathbb{R}^{n\times m}$…
We revisit the complexity of approximate pattern matching in an elastic-degenerate string. Such a string is a sequence of $n$ finite sets of strings of total length $N$, and compactly describes a collection of strings obtained by first…
The parameterized matching problem is a variant of string matching, which is to search for all parameterized occurrences of a pattern $P$ in a text $T$. In considering matching algorithms, the combinatorial natures of strings, especially…
We consider a range of simply stated dynamic data structure problems on strings. An update changes one symbol in the input and a query asks us to compute some function of the pattern of length $m$ and a substring of a longer text. We give…
Regular expressions constitute a fundamental notion in formal language theory and are frequently used in computer science to define search patterns. A classic algorithm for these problems constructs and simulates a non-deterministic finite…
We discuss the frequent pattern mining problem in a general setting. From an analysis of abstract representations, summarization and frequent pattern mining, we arrive at a generalization of the problem. Then, we show how the problem can be…
We show that the Word Problem in finitely generated subgroups of $\textsf{GL}_d(\mathbb{Z})$ can be solved in linear average-case complexity. This is done under the bit-complexity model, which accounts for the fact that large integers are…
In this paper we study a worst case to average case reduction for the problem of matrix multiplication over finite fields. Suppose we have an efficient average case algorithm, that given two random matrices $A,B$ outputs a matrix that has a…
The problem of finding factors of a text string which are identical or similar to a given pattern string is a central problem in computer science. A generalised version of this problem consists in implementing an index over the text to…
Maximum bipartite matching is a fundamental algorithmic problem which can be solved in polynomial time. We consider a natural variant in which there is a separation constraint: the vertices on one side lie on a path or a grid, and two…
A widely used method for determining the similarity of two labeled trees is to compute a maximum agreement subtree of the two trees. Previous work on this similarity measure is only concerned with the comparison of labeled trees of two…
Document listing on string collections is the task of finding all documents where a pattern appears. It is regarded as the most fundamental document retrieval problem, and is useful in various applications. Many of the fastest-growing…
Of the complex features of generic nominally-typed OO type systems, wildcard types and variance annotations are probably the hardest to fully grasp. As demonstrated when adding closures (a.k.a., lambdas) and when extending type inference in…
Cartesian tree matching is the problem of finding all substrings of a given text which have the same Cartesian trees as that of a given pattern. So far there is one linear-time solution for Cartesian tree matching, which is based on the KMP…
Pattern matching is a powerful tool which is part of many functional programming languages as well as computer algebra systems such as Mathematica. Among the existing systems, Mathematica offers the most expressive pattern matching.…
In many real-world database systems, a large fraction of the data is represented by strings: sequences of letters over some alphabet. This is because strings can easily encode data arising from different sources. It is often crucial to…
Patterns are words with terminals and variables. The language of a pattern is the set of words obtained by uniformly substituting all variables with words that contain only terminals. Length constraints restrict valid substitutions of…
We consider the design of a pattern recognition that matches templates to images, both of which are spatially sampled and encoded as temporal sequences. The image is subject to a combination of various perturbations. These include ones that…
We consider variations on the following problem: given an NFA M and a pattern p, does there exist an x in L(M) such that p matches x? We consider the restricted problem where M only accepts a finite language. We also consider the variation…