algorithm

In this paper, we present some primary methods to define a hypergroupoid by algorithm. Then, we present algorithms for checking if it is closed under ο, associativity, weak associativity, commutativity, weak commutativity, establishing the reproduction axiom, determining the type of a hypergroupoid  (H,ο) and the type of a morphism f in a hypergroupoid (H,ο). The goal of this paper is to provide algorithms for checking the basic features and morphisms in algebraic hyperstructures. Our attention is on algorithms for algebraic hyperstructures with one hyperoperation (i.e. hypergroupoids). The algorithms can be developed for other algebraic hyperstructures. 

‎A dominating set of a graph $G$ is a subset $D$ of vertices such that every vertex outside $D$ has a neighbor in $D$‎. ‎The domination number of $G$‎, ‎denoted by $\gamma(G)$‎, ‎is the minimum cardinality amongst all dominating sets of $G$‎. ‎The domination entropy of $G$‎, ‎denoted by $I_{dom}(G)$ is defined as $I_{dom}(G)=-\sum_{i=1}^k\frac{d_i(G)}{\gamma_S(G)}\log (\frac{d_i(G)}{\gamma_S(G)})$‎, ‎where $\gamma_S(G)$ is the number of all dominating sets of $G$ and $d_i(G)$ is the number of dominating sets of cardinality $i$‎. ‎A graph $G$ is $C_4$-free if it does not contain a $4$-cycle as a subgraph‎. ‎In this note we first determine the domination entropy in the graphs whose complements are $C_4$-free‎. ‎We then propose an algorithm that computes the domination entropy in any given graph‎. ‎We also consider circulant graphs $G$ and determine $d_i(G)$ under certain conditions on $i$‎.

‎In this paper‎, ‎first‎, ‎we show how to define an algebraic hyperstructure by using algorithms‎. ‎Then‎, ‎we present algorithms that calculate specific elements in algebraic hyperstructures‎. ‎These specific elements are‎: ‎scalars‎, ‎scalar identities‎, ‎identities‎, ‎inverses‎, ‎zero elements‎, ‎right simplifiable elements‎, ‎left simplifiable elements‎, ‎left absorbing-like elements and right absorbing-like elements‎. ‎We also introduce some algorithms in algebraic hyperstructures to check properties or calculate specific members‎. ‎These algorithms are presented for algebraic hyperstructures with one hyperoperation‎, ‎i.e‎. ‎hypergroupoids‎. ‎However‎, ‎they can be developed for other algebraic hyperstructures‎.

This paper focuses on a novel approach for producing a floor plan (FP), either a rectangular (RFP) or an orthogonal (OFP) based on the concept of orthogonal drawings, which satisfies the adjacency relations given by any bi-connected plane triangulation $G$.     Previous algorithms for constructing a FP are primarily restricted to the cases given below:     begin{enumerate}[(i)]         item A bi-connected plane triangulation without separating triangles (STs) and with at most 4 corner implying paths (CIPs), known as properly triangulated planar graph (PTPG).         item A bi-connected plane triangulation with an exterior face of length 3 and no CIPs, known as maximal planar graph (MPG).     end{enumerate}     The FP obtained in the above two cases is a RFP or an OFP respectively. In this paper, we present the construction of a FP (RFP if exists, else an OFP), for a bi-connected plane triangulation $G$ in linear-time.

Let $G=(V,E)$ be a graph.  A double Roman dominating function  (DRDF) of   $G $   is a function   $f:Vto {0,1,2,3}$  such that, for each $vin V$ with $f(v)=0$,  there is a vertex $u $  adjacent to $v$  with $f(u)=3$ or there are vertices $x$ and $y $  adjacent to $v$  such that  $f(x)=f(y)=2$ and for each $vin V$ with $f(v)=1$,  there is a vertex $u $    adjacent to $v$    with  $f(u)>1$.  The weight of a DRDF $f$ is   $ f (V) =sum_{ vin V} f (v)$.   Let $n$ and  $k$ be integers such that  $3leq 2k+ 1  leq n$.  The   generalized Petersen graph $GP (n, k)=(V,E) $  is the  graph  with  $V={u_1, u_2,ldots,  u_n}cup{v_1, v_2,ldots, v_n}$ and $E={u_iu_{i+1}, u_iv_i, v_iv_{i+k}:  1 leq i leq n}$, where  addition is taken  modulo $n$. In this paper,  we firstly   prove that the  decision     problem  associated with   double Roman domination is NP-omplete even restricted to planar bipartite graphs with maximum degree at most 4.  Next, we   give  a dynamic programming algorithm for  computing a minimum DRDF (i.e., a  DRDF   with minimum weight  along  all   DRDFs)  of $GP(n,k )$  in $O(n81^k)$ time and space  and so a  minimum DRDF  of $GP(n,O(1))$  can be computed in $O( n)$ time and space.

Finding a zero of a maximal monotone operator is known as one of the most impressive problems which are associated with convex analysis and mathematical optimization. Akin to this is solving the fixed point problems of the class of nonexpansive mappings, which constitutes an important part of nonlinear operators with fascinating applications in several areas such as signal processing and image restoration. This study presents a monotone hybrid algorithm for finding a common element of the zero point set of a maximal monotone operator and the fixed point set of a family of a generalized nonexpansive mapping in a Banach space. Suitable conditions under which the algorithm converges strongly are established.

The numerical approximation methods of the differential problems solution are numerous and various. Their classifications are based on several criteria: Consistency, precision, stability, convergence, dispersion, diffusion, speed and many others. For this reason a great interest must be given to the construction and the study of the associated algorithm: indeed the algorithm must be simple, robust, less expensive and fast. In this paper, after having recalled the δ-ziti method, we reformulat it to obtain an algorithm that does not require as many calculations as many nodes knowing that they are counted by thousands. We have, therefore, managed to optimize the number of iterations by passing for example from 103 at 10 iterations.

Let $G=(V,E)$ be a given graph of order $n $. A function $f : V to {0,1, 2}$ is an independent Roman dominating function (IRDF) on $G$ if for every vertex $vin V$ with $f(v)=0$ there is a vertex $u$ adjacent to $v$ with $f(u)=2$ and ${vin V:f(v)> 0}$ is an independent set. The weight of an IRDF $f$ on $G $ is the value $f(V)=sum_{vin V}f(v)$. The minimum weight of an IRDF among all IRDFs on $G$ is called the independent Roman domination number of~$G$. In this paper, we give algorithms for computing the independent Roman domination number of $G$ in $O(|V|)$ time when $G=(V,E)$ is a tree, unicyclic graph or proper interval graph.

Unlike other mathematical models, soft set theory provides a parameterization tool contribution. However, in this theory, since membership degrees are expressed as $0$ and $1$, for $(0, 1)$, we cannot determine whether any object belongs to a parameter or not. Researchers have tried to overcome this situation by ensuring that the decision maker expresses these values. However, we cannot know the accuracy of the data provided to us by the decision maker. Therefore, in this study, we introduced the concepts of relational membership function, relational non-membership function, inverse relational membership function and inverse relational non-membership function and examined the related properties of these concepts. Then, we propose two new approaches so that uncertainty can be expressed in an ideal way and can be used in decision-making. Finally, the approaches given and some of the important approaches in the literature are compared and analyzed.

Let $G=(V, E)$ be a graph. A set $S subseteq V$ is called a dominating set of $G$ if for every $vin V-S$ there is at least one vertex $u in N(v)$ such that $uin S$. The domination number of $G$, denoted by $gamma(G)$, is equal to the minimum cardinality of a dominating set in $G$. A Roman dominating function (RDF) on $G$ is a function $f:Vlongrightarrow{0,1,2}$ such that every vertex $vin V$ with $f(v)=0$ is adjacent to at least one vertex $u$ with $f(u)=2$. The weight of $f$ is the sum $f(V)=sum_{vin V}f (v)$. The minimum weight of a RDF on $G$ is the Roman domination number of $G$, denoted by $gamma_R(G)$. A graph $G$ is a Roman Graph if $gamma_R(G)=2gamma(G)$. In this paper, we first study the complexity issue of the problem posed in [E.J. Cockayane, P.M. Dreyer Jr., S.M. Hedetniemi and S.T. Hedetniemi, On Roman domination in graphs, textit{Discrete Math.} 278 (2004), 11--22], and show that the problem of deciding whether a given graph is a Roman graph is NP-hard even when restricted to chordal graphs. Then, we give linear algorithms that compute the domination number and the Roman domination number of a given unicyclic graph. Finally, using these algorithms we give a linear algorithm that decides whether a given unicyclic graph is a Roman graph.

In this paper, we try to find the inverse for a general r- diagonal matrix (band matrix) by an algorithm. We did this work by LU factorization and a lemma about these matrices. This work can decrease the computational cost in compare with general inverse algorithm. We show a numerical example for clear this method.

There is a plethora of third and fourth convergence order algorithms  for solving Banach space valued equations. These orders are shown under conditions on higher than one derivatives not appearing on these algorithms. Moreover, error estimations on the distances involved or  uniqueness of the solution results if given at all are also based on the existence of high order derivatives. But these problems limit the applicability  of the algorithms. That is why we address all these problems under  conditions only on the first derivative that appear in these algorithms. Our analysis includes computable error estimations as well as uniqueness results based on $omega-$ continuity conditions on the Fr'echet derivative of the operator involved.

The objective of this research is to design and implement a computational model to determine DNA barcodes by utilizing the Particle Swarm Optimization (PSO) algorithms implemented on Big Data Platforms, namely Apache Hadoop and Apache Spark. The steps are as follows: (i) inputting DNA sequences to Hadoop Distributed File System (HDFS) in Apache Hadoop, (ii) pre-processing data, (iii) implementing PSO by utilizing the User Defined Function (UDF) in Apache Spark, (iv) collecting results and saving to HDFS. After obtaining the computational model, two following simulations have been done: the first scenario is using 4 cores and several worker nodes, meanwhile the second one consists of a cluster with 2 worker nodes and several cores. In term of computational time, the results show a significant acceleration between standalone and big data platforms with both experimental scenarios. This study proves that the computational model built on the big data platform shows the development of features and acceleration of previous research.

The unit disk graph is used to model a wireless sensor network when all sensors have the same communication radius. Hence, the following two optimization problems have been investigated by the researchers: maximal independent set in the network and minimal network dominating set. Since these problems are Np-hard, several algorithms have been presented for their approximation. In this paper, we have presented a honeycomb graph and algorithmic matrix methods for approximating the maximal independent set in the network. Finally, we have confirmed the validity of the algorithm and its complexity and studied it with a numerical example. Keywords: Wireless network, Independent set, Dominating set, Algorithm, Honeycomb network E. Leeuwen, Approximation Algorithms for Unit Disk Graphs, technical report, institute of information and computing sciences, utrecht university, (2004), UU-CS-2004-066. N. Bourgeois, F. Della Croce, B. Escoffier. V.Th. Paschos, Fast algorithms for min independent dominating set, Discrete Applied Mathematics 161, (2013), pp. 558-572

In this research study, we present a novel frame work for handling bipolar fuzzy soft information by combining bipolar fuzzy soft sets with graphs.
We introduce several basic notions concerning bipolar fuzzy soft graphs and investigate some related properties.
We also consider the application of the bipolar fuzzy soft graphs. In particular, three efficient algorithms are developed to solve multiple criteria decision-making problems regarding social network, investment in shares and detection of bipolar disorder in children.

In this paper, we define an H(·, ·)-mixed relaxed co-ηmonotone mapping and we apply the same for solving a resolvent equation problem in Hilbert spaces. We also prove some of the properties of H(·, ·)-mixed relaxed co-η-monotone mapping. A mann-type iterative algorithm is developed to approximate the solution of resolvent equation problem. Convergence of the iterative sequences is also demonstrated. In support of the concept of H(·, ·)-mixed relaxed co-η-monotone mapping, we construct an example.

In this paper, we introduce and study fuzzy variational-like inclusion, fuzzy resolvent equation and $H(cdot,cdot)$-$phi$-$eta$-accretive operator in real uniformly smooth Banach spaces. It is established that fuzzy variational-like inclusion is equivalent to a fixed point problem as well as to a fuzzy resolvent equation. This equivalence is used to define an iterative algorithm for solving fuzzy resolvent equation. Some examples are given.