Related papers: Minor complexities of finite operations

We study connectivity functions, that is, integer-valued symmetric submodular functions on a finite ground set attaining $0$ on the empty set. For a connectivity function $f$ on an $n$-element set $V$ and an integer $k\ge 0$, we show that…

The article concerns low-rank approximation of matrices generated by sampling a smooth function of two $m$-dimensional variables. We identify several misconceptions surrounding a claim that, for a specific class of analytic functions, such…

We introduce a new logic for describing properties of graphs, which we call low rank MSO. This is the fragment of monadic second-order logic in which set quantification is restricted to vertex sets of bounded cutrank. We prove the following…

The main result is that: function descriptions are not made equal, and they can be categorised in at least two categories using various computational methods for function evaluation. The result affects Kolmogorov complexity and Random…

Infinite words, also known as streams, hold significant interest in computer science and mathematics, raising the natural question of how their complexity should be measured. We introduce cellular automaton reducibility as a measure of…

Locating-dominating codes have been studied widely since their introduction in the 1980s by Slater and Rall. In this paper, we concentrate on vertices that must belong to all minimum locating-dominating codes in a graph. We call them…

Classification is a central problem for dynamical systems, in particular for families that arise in a wide range of topics, like substitution subshifts. It is important to be able to distinguish whether two such subshifts are isomorphic,…

Let $\mathcal{G}$ be a minor-closed graph class. We say that a graph $G$ is a $k$-apex of $\mathcal{G}$ if $G$ contains a set $S$ of at most $k$ vertices such that $G\setminus S$ belongs to $\mathcal{G}.$ We denote by $\mathcal{A}_k…

In this thesis, a detailed study shows that closed itemsets and minimal generators play a key role for concisely representing both frequent itemsets and association rules. These itemsets structure the search space into equivalence classes…

Complex networks with high numbers of nodes or links are often difficult to analyse. However, not all elements contribute equally to their structural patterns. A small number of elements (the hubs) seem to play a particularly relevant role…

The present paper is the first one in the sequence of papers about a simple class of {\em framed $4$-graphs}; the goal of the present paper is to collect some well-known results on planarity and to reformulate them in the language of {\em…

In this self-contained paper, we present a theory of the piecewise linear minimal valid functions for the 1-row Gomory-Johnson infinite group problem. The non-extreme minimal valid functions are those that admit effective perturbations. We…

Let $G=(V,E)$ be a graph. An ordering of $G$ is a bijection $\alpha: V\dom \{1,2,..., |V|\}.$ For a vertex $v$ in $G$, its closed neighborhood is $N[v]=\{u\in V: uv\in E\}\cup \{v\}.$ The profile of an ordering $\alpha$ of $G$ is…

We determine sufficient conditions under which certain recursively defined functions are well defined for all real inputs. Given a function $f:\mathbb R\to\mathbb R$, call a decreasing sequence $x_1>x_2>x_3>\cdots$ "$f$-bad" if…

We describe a method for approximating a single-variable function $f$ using persistence diagrams of sublevel sets of $f$ from height functions in different directions. We provide algorithms for the piecewise linear case and for the smooth…

For compact sets $K\subset \mathbb C^{d}$, we introduce a subalgebra $A_{D}(K)$ of $A(K)$, which allows us to obtain Mergelyan type theorems for products of planar compact sets as well as for graphs of functions.

An important first step in computational SAR modeling is to transform the compounds into a representation that can be processed by predictive modeling techniques. This is typically a feature vector where each feature indicates the presence…

A new class of functions is presented. The structure of the algorithm, particularly the selection criteria (branching), is used to define the fundamental property of the new class. The most interesting property of the new functions is that…

In this paper we study the separation between the deterministic (classical) query complexity ($D$) and the exact quantum query complexity ($Q_E$) of several Boolean function classes using the parity decision tree method. We first define the…

A possible world of an incomplete database table is obtained by imputing values from the attributes (infinite) domain to the place of \texttt{NULL} s. A table satisfies a possible key or possible functional dependency constraint if there…