Related papers: Independent sets of closure operations
The objective of this article is to formalize the definition of NP problems. We construct a mathematical model of discrete problems as independence systems with weighted elements. We introduce two auxiliary sets that characterize the…
In this paper we introduce the concept of completeness of sets. We study this property on the set of integers. We examine how this property is preserved as we carry out various operations compatible with sets. We also introduce the problem…
Numerous applications in scheduling, such as resource allocation or steel manufacturing, can be modeled using the NP-hard Independent Set problem (given an undirected graph and an integer k, find a set of at least k pairwise non-adjacent…
We settle the complexity of the Independent Set Reconfiguration problem on bipartite graphs under all three commonly studied reconfiguration models. We show that under the token jumping or token addition/removal model the problem is…
We prove some unconditional cases of the Existential Closedness problem for the modular $j$-function. For this, we show that for any finitely generated field we can find a "convenient" set of generators. This is done by showing that in any…
The concept of decomposition in computer science and engineering is considered a fundamental component of computational thinking and is prevalent in design of algorithms, software construction, hardware design, and more. We propose a simple…
We define the parametric closure problem, in which the input is a partially ordered set whose elements have linearly varying weights and the goal is to compute the sequence of minimum-weight lower sets of the partial order as the weights…
We introduce two closure operations on ideals in commutative rings related to the ring operation of root closure. One closure is the result of iterating a root-like operation on ideals infinitely many times, and the other closure arises as…
Suppose that we are given two independent sets I_b and I_r of a graph such that |I_b|=|I_r|, and imagine that a token is placed on each vertex in |I_b|. Then, the sliding token problem is to determine whether there exists a sequence of…
Discovering patterns in a sequence is an important aspect of data mining. One popular choice of such patterns are episodes, patterns in sequential data describing events that often occur in the vicinity of each other. Episodes also enforce…
We investigate uniqueness problems for an entire function that shares two small functions of finite order with their difference operators. In particular, we give a generalization of a result in $[2]$.
Recoverable algorithms tolerate failures and recoveries of processes by using non-volatile memory. Of particular interest are self-implementations of key operations, in which a recoverable operation is implemented from its non-recoverable…
We investigate inference of variable-length codes in other domains of computer science, such as noisy information transmission or information retrieval-storage: in such topics, traditionally mostly constant-length codewords act. The study…
The maximum independent set problem is known to be NP-hard in the class of subcubic graphs, i.e. graphs of vertex degree at most 3. We present a polynomial-time solution in a subclass of subcubic graphs generalizing several previously known…
We investigate the algebraic structure on the set of closure operations of a ring. We show the set of closure operations is not a monoid under composition for a discrete valuation ring. Even the set of semiprime operations over a DVR is not…
We consider optimization algorithms that are open systems, that is, with external inputs and outputs. Such algorithms arise for instance, when analyzing the effect of noise or disturbance on an algorithm, or when an algorithm is part of…
Let $A\subseteq B$ be a ring extension and $\mathcal{G}$ be a set of $A$-submodules of $B$. We introduce a class of closure operations on $\mathcal{G}$ (which we call \emph{multiplicative operations on $(A,B,\mathcal{G})$}) that generalizes…
Multisets are an intuitive extension of the traditional concept of sets that allow repetition of elements, with the number of times each element appears being understood as the respective multiplicity. Recent generalizations of multisets to…
We continue work on the topology obtained by the convergence $\lambda_{ls}$, which started in \cite{KuPaCZ}, and further investigated in \cite{KuPaFil19}. The main goal is to describe the closed sets and closure operator by the family of…
An open (resp., closed) subset A of a topological space (X, T ) is called C-open (resp., C-closed) set if cl(A) \ A (resp., A \ int(A)) is a countable set. This paper aims to present the concept of C-open and C-closed sets. We first…