Journal of Algorithms and Computation
Volume:51 Issue: 2, Dec 2019

vspace{0.2cm} Let $G$ be a graph and $f:V(G)rightarrow {1,2,3,.....left|V(G)right|}$ be a bijection. Let $p_{uv}=f(u)f(v)$ and\ $ d_{uv}= begin{cases} left[frac{f(u)}{f(v)}right] ~~if~~ f(u) geq f(v)\ \ left[frac{f(v)}{f(u)}right] ~~if~~ f(v) geq f(u)\ end{cases} $\ for all edge $uv in E(G)$. For each edge $uv$ assign the label $1$ if $gcd (p_{uv}, d_{uv})=1$ or $0$ otherwise. $f$ is called PD-prime cordial labeling if $left|e_{f}left(0right)-e_{f}left(1right) right| leq 1$ where $e_{f}left(0right)$ and $e_{f}left(1right)$ respectively denote the number of edges labelled with $0$ and $1$. A graph with admit a PD-prime cordial labeling is called PD-prime cordial graph. & & vspace{0.2cm}.The formula is not displayed correctly!

vspace{0.2cm}In this paper, we design a data structure for the following problem. Let $pi$ be an $x$-monotone trajectory with $n$ vertices in the plane and $epsilon >0$. We show how to preprocess $pi$ and $epsilon$ into a data structure such that for any horizontal query segment $Q$ in the plane, one can quickly determine the minimal continuous fraction of $pi$ whose Fr{'e}chet and Hausdorff distance to the horizontal query segment $Q$ is at most some threshold value $epsilon$. We present a data structure for this query that needs $mathcal{O}(nlog{}n)$ preprocessing time, $mathcal{O}(n)$ space, and $mathcal{O}(log{} n)$ query time. & & vspace{0.2cm}

In this paper, a type of fuzzy system is investigated in which the feasible region is formed as the intersection of two types of fuzzy inequalities and “Fuzzy Or” is considered as fuzzy composition. Some theoretical properties are derived and four necessary and sufficient conditions are presented. Moreover, an algorithm is proposed to solve the problem and an example is described to illustrate the algorithm.

In this paper, we introduce a family of graphs which is a generalization of zero-divisor graphs and compute an upper-bound for the diameter of such graphs. We also investigate their cycles and cores

We study the problem of computing the diameter of a  set of $n$ points in $d$-dimensional Euclidean space for a fixed dimension $d$, and propose a new $(1+varepsilon)$-approximation algorithm with $O(n+ 1/varepsilon^{d-1})$ time and $O(n)$ space, where $0 < varepsilonleqslant 1$. We also show that the proposed algorithm can be modified to a $(1+O(varepsilon))$-approximation algorithm with $O(n+ 1/varepsilon^{frac{2d}{3}-frac{1}{2}})$ running time. Our proposed algorithms are different with the previous algorithms in terms of computational technique and data structures. These results provide some improvements in comparison with existing algorithms in terms of simplicity and data structure.The formula is not displayed correctly!

An outer connected dominating(OCD) set of a graph $G=(V,E)$ is a set $tilde{D} subseteq V$ such that every vertex not in $S$ is adjacent to a vertex in $S$, and the induced subgraph of $G$ by $V setminus tilde{D}$, i.e. $G [V setminus tilde{D}]$, is connected. The OCD number of $G$ is the smallest cardinality of an OCD set of $G$. The outer-connected bondage number of a nonempty graph G is the smallest number of edges whose removal from G results in a graph with a larger OCD number. Also, the outer-connected reinforcement number of G is the smallest number of edges whose addition to G results in a graph with a smaller OCD number. In 2018, Hashemi et al. demonstrated that the decision problems for the Outer-Connected Bondage and the Outer-Connected Reinforcement numbers are all NP-hard in general graphs. In this paper, we improve these results and show their hardness for bipartite graphs. Also, we obtain bounds for the outer-connected bondage number.The formula is not displayed correctly!

vspace {0.2cm}Suppose $G$ is a simple and connected graph. The first and second Zagreb indices of $G$ are two degree-based graph invariants defined as $M_1(G) = sum_{v in V(G)}deg(v)^2$ and $M_2(G) = sum_{e=uv in E(G)}deg(u)deg(v)$, respectively. The graph $G$ is called $p-$quasi $k-$cyclic, if there exists a subset $S$ of vertices such that $|S| = p$, $G setminus S$ is $k-$cyclic and there is no a subset $S^prime$ of $V(G)$ such that $|S^prime| < |S|$ and $G setminus S^prime$ is $k-$cyclic. The aim of this paper is to characterize all graphs with maximum values of Zagreb indices among all $p-$quasi $k-$cyclic graphs with $k leq 3$. & & vspace{0.2cm}.The formula is not displayed correctly!

Analyzing eyes performance is essential for effective functioning of human. Therefore, following their motion could help doctors to make quick and accurate diagnoses for disorders like Autism, schizophrenia, or attention deficit hyperactivity disorder. Recently, several studies investigated autism disorder diagnosis and treatment. Meanwhile, various algorithms have been provided for eye tracking. In this paper, it is intended to identify diagnosis parameters of autism disorder using eye tracking concept. The eye tracking algorithm that has been used in this research is simple and sufficient accurate to appropriate function on videos with varying quality. The direct analysis of gaze and study of the interactions of its features are employed a useful method for diagnosis of autism. For this purpose, two separate groups of ordinary children and children with autism are considered. By tracking their eyes while watching television and performing the necessary analyses then their eye movements are compared and discussed. To identify pupils is face detection Viola Jones algorithm is implemented.

Let $S$ be a set of imprecise points that is represented by axis-aligned pairwise disjoint squares in the plane. A precise instance of $S$ is a set of points, one from each region of $S$. In this paper, we study the optimal minimum spanning tree (textit{OptMST}) problem on $S$. The textit{OptMST} problem looks for the precise instance of $S$ such that the weight of the MST in this instance, maximize (Max-MST) or minimize (Min-MST) between all precise instances of~$S$ under $L_1$-metric. We present a $(frac{3}{7})$-approximation algorithm for Max-MST. This is an improvement on the best-known approximation factor of $1/3$. If $S$ satisfies $k$-separability property (the distance between any pair of squares are at least $k.a_{max}$ where $a_{max}$ is the maximum length of the squares), the factor parameterizes to $frac{2k+3}{2k+7}$. We propose a new lower bound for Min-MST problem on $S$ under $L_1$-metric where $S$ contains unit squares and provide an approximation algorithm with $(1+2sqrt{2})$ asymptotic factor.the formula is not displayed correctly!

Over the recent years, many research has been carried out on applying the optimization approach to science and engineering problems. Thereby, numerous metaheuristic algorithms have been developed for solving such type of challenge. Despite an increase in the number of these algorithms, there is currently no specific algorithm which can be employed to optimize all varieties of problems. In the current research, a novel metaheuristic algorithm for global and continuous nonlinear optimization, named as Xerus Optimization Algorithm (XOA) has been introduced. XOA has been inspired by group living and lifestyle of cape ground squirrels (Xerus inauris), by taking into account their co-operation in living together, hunting, and communication, etc. In order to evaluate the efficiency of XOA, algorithms for 30 different benchmarks have been analyzed and compared to some novel and renowned metaheuristic algorithms. The simulation response illustrates a significant improvement in  the performance of the novel XOA, in comparison to the algorithms presented in the literature. The proposed algorithm can be employed for many applications that require a solution to different optimization problems.

The tenacity of a graph $G$, $T(G)$, is defined by$T(G) = min{frac{mid Smid +tau(G-S)}{omega(G-S)}}$, where theminimum is taken over all vertex cutsets $S$ of $G$. We define$tau(G - S)$ to be the number of the vertices in the largestcomponent of the graph $G-S$, and $omega(G-S)$ be the number ofcomponents of $G-S$. In this paperwe consider the relationship between the minimum degree $delta (G)$ of a graph and the complexityof recognizing if a graph is $T$-tenacious. Let $Tgeq 1$ be a rational number. We first show that if$delta(G)geq frac{Tn}{T+1}$, then $G$ is $T$-tenacious. On the other hand, for any fixed $epsilon>0$, weshow that it is $NP$-hard to determine if $G$ is $T$-tenacious, even for the class of graphs with $delta(G)geq(frac{T}{T+1}-epsilon )n$.the formula is not displayed correctly!

A data-intensive computing platform, encountered in some grid and cloud computing applications, includes numerous tasks that process, transfer or analysis large data files. In such environments, there are large and geographically distributed users that need these huge data. Data management is one of the main challenges of distributed computing environment since data plays on devoted role. Dynamic data replication techniques have been widely applied to improve data access and availability. In order to introduce an appropriate data replication algorithm, there are four important problems that must be solved. 1) Which file should be replicated; 2) How many suitable new replicas should be stored; 3) Where the new replicas should be placed; 4) Which replica should be deleted to make room for new copies. In this paper, we focus particularly on replica replacement issue which makes a significant difference in the efficiency of replication algorithm. We survey replica replacement approaches (from 2004 to 2018) that are developed for both grid and cloud environments. The presented review illustrates the replica replacement problem from a technological and it differs significantly from previous reviews in terms of comprehensiveness and integrated discussion. In this paper, we present different parameters involved in replacement process and show the key points of the recent algorithms with a tabular representation of all those factors. We also report open issues and new challenges in the area.