950 Results Found

NP-complete problems in graphs, such as enumeration and the selection of subgraphs with given characteristics, become especially relevant for large graphs and networks. Herein, particular statements with constraints are proposed to solve such problem...

This paper is a continuation of our previous publication of enhanced matrix power function (MPF) as a conjectured one-way function. We are considering a problem introduced in our previous paper and prove that tis problem is NP-Complete. The proof is...

This study addresses the growing need to convert unstructured legal and policy documents into formal computational models that support transparent decision-making. The purpose of the work is to develop an applied framework that connects Legal NLP and...

In this paper we present a cryptographic primitive based on non-commutative cryptography. This primitive is used for key exchange protocol (KEP) construction. We prove that the security of this primitive relies on a nondeterministic polynomial comple...

The Solution of the Subproblem of the Cutting Angle Method of Global Optimization for problems of minimizing increasing Positively Homogeneous of degree one functions is proved to be NP-Complete. For the proof of this fact we formulate another proble...

A dominating set of a graph is a subset of vertices such that every vertex is either contained in the set or adjacent to at least one vertex in it. A dominating set is called k-fair if each vertex not in this set is adjacent to exactly k vertices of...

In this work, we investigate the variant of the Internet Shopping Optimization Problem (ISHOP) that considers different item units. This variant is more challenging than the original problem. The original ISHOP is already known as a combinatorial NP-...

We investigate the computational complexity of deciding whether a given univariate integer polynomial $p\left(x\right)$ has a factor $q\left(x\right)$ satisfying specific additional constraints. When the only constraint imposed on $q\left(x\right)$ is to have a degree smaller than the deg...

Several variants of the edit distance problem with block deletions are considered. Polynomial time optimal algorithms are presented for the edit distance with block deletions allowing character insertions and character moves, but without block moves....

Analysis of the currently established Bayesian nearest neighbors classification model points to a connection between the computation of its normalizing constant and issues of NP-completeness. An alternative predictive model constructed by aggregating...

In this paper we consider general continuous propositional logics and prove some basic properties about them. First, we characterize full systems of continuous connectives of the form $\{\neg ,\dot{-},f\}$ where f is a unary connective. We also show that...

P systems have been known to provide efficient polynomial (often linear) deterministic solutions to hard problems. In particular, cP systems have been shown to provide very crisp and efficient solutions to such problems, which are typically linear wi...

This paper proposes a quantum algorithm, named Dicke state quantum search (DSQS), to set qubits in the Dicke state $|D_k^n⟩$ of D states in superposition to locate the target inputs or solutions of specific patterns among $2^n$ unstructured input ins...

A planar 3-index assignment problem (P3AP) of size n is an NP-complete problem. Its global optimal solution can be determined by a branch and bound algorithm. The efficiency of t...

For a simple graph $G=(V,E)$ with no isolated vertices, a total Roman {3}-dominating function(TR3DF) on G is a function $f:V\left(G\right)\to \{0,1,2,3\}$ having the property that (i) ${\sum }_{w\in N\left(v\right)}f\left(w\right)\ge 3$ if $f\left(v\right)=0$; (ii) ${\sum }_{w\in N\left(v\right)}f\left(w\right)\ge 2$ if $f\left(v\right)=1$; and (iii) every vertex v with $f$...

This paper provides an initial introduction to, and definition of, the ‘Dynamically Powered Relays for a Flexible Optical Network’ (DPR-FON) problem for opto-electro-optical (OEO) regenerators used in optical networks. In such networks, optical trans...

The maximum clique problem is a problem that takes many forms in optimization and related graph theory problems, and also has many applications. Because of its NP-completeness (nondeterministic polynomial time), the question arises of its solvability...

A total k-rainbow dominating function on a graph $G=(V,E)$ is a function $f:V\left(G\right)\to 2^{\{1,2,\dots ,k\}}$ such that (i) ${\cup }_{u\in N\left(v\right)}f\left(u\right)=\{1,2,\dots ,k\}$ for every vertex v with $f\left(v\right)=\varnothing$, (ii) ${\cup }_{u\in N\left(v\right)}f\left(u\right)\ne \varnothing$ for $f\left(v\right)\ne \varnothing$. T...

This paper studies subset construction in NP-complete problems from the perspective of structured exploration of combinatorial search spaces. Classical approaches rely on exhaustive enumeration of subsets, which leads to exponential growth in time an...

Topology control is one of the most essential technologies in wireless sensor networks (WSNs); it constructs networks with certain characteristics through the usage of some approaches, such as power control and channel assignment, thereby reducing th...

A total perfect Roman dominating function (TPRDF) on a graph $G=(V,E)$ is a function f from V to $\{0,1,2\}$ satisfying (i) every vertex v with $f\left(v\right)=0$ is a neighbor of exactly one vertex u with $f\left(u\right)=2$; in addition, (ii) the subgraph of G that is induced by...

Cloud computing is one of the most commonly used infrastructures for carrying out activities using virtual machines known as processing units. One of the most fundamental issues with cloud computing is task scheduling. The optimal determination of sc...

A perfect Italian dominating function assigns values in $\{0,1,2\}$ to the vertices of a graph so that every zero-valued vertex has a neighbor-value sum of exactly two. We determine the computational complexity of the problem for bipartite graphs whose n...

The celebrated question of whether $P=NP$ continues to define the boundary between the feasible and the intractable in computer science. In this paper, we revisit the problem from two complementary angles: Time-Relative Description Complexity and autom...

The clique transversal problem and its variants have garnered significant attention in the last two decades due to their practical applications in communication networks, social-network theory and transceiver placement for cellular telephones. While...

The unbalanced assignment problem (UAP) is to optimally resolve the problem of assigning n jobs to m individuals (m < n), such that minimum cost or maximum profit obtained. It is a vitally important Non-deterministic Polynomial (NP) complete probl...

This paper explores the computational challenges of clique transversal problems in d-degenerate graphs, which are commonly encountered across theoretical computer science and various network applications. We examine d-degenerate graphs to highlight t...

In the context of defining $\mathcal{NP}$-completeness, a tableau represents a hypothetical accepting computation path p of a nondeterministic polynomial time Turing machine N on an input w. The tableau is encoded by the propositional logic formula $\psi$, define...

Over the years, spiking neural P systems (SNPS) have grown into a popular model in membrane computing because of their diverse range of applications. In this paper, we give a comprehensive summary of applications of SNPS and its variants, especially...

The computation of distances between strings has applications in molecular biology, music theory and pattern recognition. One such measure, called short reversal distance, has applications in evolutionary distance computation. It has been shown that...

A new graph parameter, edge neighbor toughness is introduced to measure how difficult it is for a graph to be broken into many components through the deletion of the closed neighborhoods of a few edges. Let $G=(V,E)$ be a graph. An edge e is said to be...

This paper proposes a reliable network interdiction model with multiple unit costs, which maximizes the minimum arrival cost of the invader to the sink by setting obstacles on some arcs with limited resources in the given network. In other words, giv...

The open shop scheduling problem (OSSP) is one of the standard scheduling problems. It consists of scheduling jobs associated with a finite set of tasks developed by different machines. In this case, each machine processes at most one operation at a...

Dimension reduction is a technique used to transform data from a high-dimensional space into a lower-dimensional space, aiming to retain as much of the original information as possible. This approach is crucial in many disciplines like engineering, b...

We consider the coordination of transportation and batching scheduling with one single vehicle for minimizing total weighted completion time. The computational complexity of the problem with batch capacity of at least 2 was posed as open in the liter...

We present a technique to solve the linear integer model with variable bounding. By using the continuous optimal solution of the linear integer model, the variable bounds for the basic variables are approximated and then used to calculate the optimal...

As a contribution to automated set-theoretic inferencing, a translation is proposed of conjunctions of literals of the forms $x=y\setminus z$, $x\ne y\setminus z$, and $z=\left\{x\right\}$, where $x,y,z$ stand for variables ranging over the von Neumann universe of sets, into qua...

Considering a class $\mathcal{R}$ comprising recognizer membrane systems with the capability of providing polynomial-time and uniform solutions for NP-complete problems (referred to as a “presumably efficient” class), the corresponding poly...

Supergrid graphs are derived by computing stitch paths for computerized embroidery machines. In the past, we have studied the Hamiltonian-related properties of supergrid graphs and their subclasses of graphs. In this paper, we propose a generalized g...

Perfect Roman Dominating Functions and Unique Response Roman Dominating Functions are two ways to translate perfect code into the framework of Roman Dominating Functions. We also consider the enumeration of minimal Perfect Roman Dominating Functions...

Using assembly theory, we investigate the assembly pathways of binary strings (bitstrings) of length N formed by joining bits present in the assembly pool and the bitstrings that entered the pool as a result of previous joining operations. We show th...

The SAT problem is maybe one of the most famous NP-complete problems. This paper deals with the 3-SAT problem. We follow a sort of incremental strategy to save computational costs with respect to the classical quantum computing approach. We present a...

P systems with mitochondria enzymes layer computing is a recent version of P systems; it integrates a new feature inspired from the enzymes gate of a natural cell to the cell-like P systems. The model of a computational layer is well known as a probl...

A (1,0)-super solution is a satisfying assignment such that if the value of any one variable is flipped to the opposite value, the new assignment is still a satisfying assignment. Namely, every clause must contain at least two satisfied literals. Bec...

Course timetabling is a combinatorial optimization problem and has been confirmed to be an NP-complete problem. Course timetabling problems are different for different universities. The studied university course timetabling problem involves hard cons...

In this paper we introduce aspBEEF, a tool for generating explanations for the outcome of an arbitrary machine learning classifier. This is done using Grover’s et al. framework known as Balanced English Explanations of Forecasts (BEEF) that gen...

The Disjoint Connecting Paths problem and its capacitated generalization, called Unsplittable Flow problem, play an important role in practical applications such as communication network design and routing. These tasks are NP-hard in general, but var...

The article formulates the Dictionary Recognition problem, which is relevant for a wide range of applied problems: word recognition in a noisy audio signal for natural language processing tasks or in a noisy electromagnetic signal, recognition of vis...

Synthesis of time-triggered network schedules is a known practice to obtain low jitter and bounded end-to-end delay needed in some applications where not only the information but the transmission timings are crucial. However, synthesizing such schedu...

The domatic partition problem consists of partitioning a given graph into a maximum number of disjoint dominating sets. This problem is related with the domatic number problem, which consists of quantifying this maximum number of disjoint dominating...