Related papers: The Swap Matching Problem Revisited
In this paper we present a new problem, the fast set intersection problem, which is to preprocess a collection of sets in order to efficiently report the intersection of any two sets in the collection. In addition we suggest new solutions…
Given a text and a pattern over an alphabet, the pattern matching problem searches for all occurrences of the pattern in the text. An equivalence relation $\approx$ is called a substring consistent equivalence relation (SCER), if for two…
This paper addresses the challenging problem of retrieval and matching of graph structured objects, and makes two key contributions. First, we demonstrate how Graph Neural Networks (GNN), which have emerged as an effective model for various…
This paper presents a new combinatorial optimisation task, the Subset Sum Matching Problem (SSMP), which is an abstraction of common financial applications such as trades reconciliation. We present three algorithms, two suboptimal and one…
Graph pattern matching is a routine process for a wide variety of applications such as social network analysis. It is typically defined in terms of subgraph isomorphism which is NP-Complete. To lower its complexity, many extensions of graph…
The problem of finding a maximum size matching in a graph (known as the maximum matching problem) is one of the most classical problems in computer science. Despite a significant body of work dedicated to the study of this problem in the…
Given a pattern string $P$ of length $n$ and a query string $T$ of length $m$, where the characters of $P$ and $T$ are drawn from an alphabet of size $\Delta$, the {\em exact string matching} problem consists of finding all occurrences of…
String matching is the problem of finding all the substrings of a text which match a given pattern. It is one of the most investigated problems in computer science, mainly due to its very diverse applications in several fields. Recently,…
In this paper, we extend the notion of gapped strings to elastic-degenerate strings. An elastic-degenerate string can been seen as an ordered collection of k > 1 seeds (substrings/subpatterns) interleaved by elastic-degenerate symbols such…
The classical pattern matching paradigm is that of seeking occurrences of one string - the pattern, in another - the text, where both strings are drawn from an alphabet set $\Sigma$. Assuming the text length is $n$ and the pattern length is…
We study the complexity of the problem of searching for a set of patterns that separate two given sets of strings. This problem has applications in a wide variety of areas, most notably in data mining, computational biology, and in…
Fast matching of regular expressions with bounded repetition, aka counting, such as (ab){50,100}, i.e., matching linear in the length of the text and independent of the repetition bounds, has been an open problem for at least two decades.…
A pattern $\alpha$ is a string of variables and terminal letters. We say that $\alpha$ matches a word $w$, consisting only of terminal letters, if $w$ can be obtained by replacing the variables of $\alpha$ by terminal words. The matching…
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.…
Graph matching aims to find correspondences between two graphs. It is a fundamental task in pattern recognition. The classical spectral matching algorithm has time complexity $\mathcal{O}(n^4)$ and space complexity $\mathcal{O}(n^4)$, where…
A pattern $\alpha$ is a string of variables and terminal letters. We say that $\alpha$ matches a word $w$, consisting only of terminal letters, if $w$ can be obtained by replacing the variables of $\alpha$ by terminal words. The matching…
Subgraph matching is a compute-intensive problem that asks to enumerate all the isomorphic embeddings of a query graph within a data graph. This problem is generally solved with backtracking, which recursively evolves every possible partial…
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…
Graph matching, also known as network alignment, refers to finding a bijection between the vertex sets of two given graphs so as to maximally align their edges. This fundamental computational problem arises frequently in multiple fields…
We propose a fast approximate algorithm for large graph matching. A new projected fixed-point method is defined and a new doubly stochastic projection is adopted to derive the algorithm. Previous graph matching algorithms suffer from high…