Related papers: Fractal Word Search: How Deep to Delve
This work proposes a variable neighbourhood search (FTS) that uses a fractal-based local search primarily designed for images. Searching for specific content in images is posed as an optimisation problem, where evidence elements are…
The complexity function of an infinite word $w$ on a finite alphabet $A$ is the sequence counting, for each non-negative $n$, the number of words of length $n$ on the alphabet $A$ that are factors of the infinite word $w$. The goal of this…
Partial words are sequences over a finite alphabet that may contain wildcard symbols, called holes, which match or are compatible with all letters; partial words without holes are said to be full words (or simply words). Given an infinite…
We study the fractal structure of language, aiming to provide a precise formalism for quantifying properties that may have been previously suspected but not formally shown. We establish that language is: (1) self-similar, exhibiting…
An approximate textual retrieval algorithm for searching sources with high levels of defects is presented. It considers splitting the words in a query into two overlapping segments and subsequently building composite regular expressions…
As large language models (LLMs) are increasingly deployed across diverse domains, ensuring their safety has become a critical concern. In response, studies on jailbreak attacks have been actively growing. Existing approaches typically rely…
A set X of partial words over a finite alphabet A is called unavoidable if every two-sided infinite word over A has a factor compatible with an element of X. Unlike the case of a set of words without holes, the problem of deciding whether…
Full-text search engines are important tools for information retrieval. In a proximity full-text search, a document is relevant if it contains query terms near each other, especially if the query terms are frequently occurring words. For…
A layerwise search in a split-by-edges tree (as defined by Br{\ae}ndeland, 2015) of agiven graph produces a maximum independent set in exponential time. A depth-first search produces an independent set, which may or may not be a maximum, in…
The avoidability, or unavoidability of patterns in words over finite alphabets has been studied extensively. A word (pattern) over a finite set is said to be unavoidable if, for all but finitely many words, there exists a morphism mapping…
A fractal bears a complex structure that is reflected in a scaling hierarchy, indicating that there are far more small things than large ones. This scaling hierarchy can be effectively derived using head/tail breaks - a clustering and…
Anytime heuristic search algorithms try to find a (potentially suboptimal) solution as quickly as possible and then work to find better and better solutions until an optimal solution is obtained or time is exhausted. The most widely-known…
This paper is a sharp and focussed exploration of the Fibonacci substitution and the mathematical entity it gives rise to, the Fibonacci word. Our investigations are both of an algebraic and a geometric nature. Indeed, it is the combination…
Fractals are geometric shapes that can display complex and self-similar patterns found in nature (e.g., clouds and plants). Recent works in visual recognition have leveraged this property to create random fractal images for model…
We study algorithmic problems on subsets of Euclidean space of low fractal dimension. These spaces are the subject of intensive study in various branches of mathematics, including geometry, topology, and measure theory. There are several…
A search query consists of several words. In a proximity full-text search, we want to find documents that contain these words near each other. This task requires much time when the query consists of high-frequently occurring words. If we…
We introduce an algorithm for a search of extremal fractal curves in large curve classes. It heavily uses SAT-solvers~ -- heuristic algorithms that find models for CNF boolean formulas. Our algorithm was implemented and applied to the…
Analysis and modeling of networked objects are fundamental pieces of modern data mining. Most real-world networks, from biological to social ones, are known to have common structural properties. These properties allow us to model the growth…
Solving inverse problems in natural sciences often requires a search pro- cess to find explanatory models that match collected field data. Inverse problems are often under-determined meaning that there are many poten- tial explanatory…
Considering a 2D matrix of positive and negative numbers, how might one draw a rectangle within it whose contents sum higher than all other rectangles'? This fundamental problem, commonly known the maximum rectangle problem or subwindow…