JOURNAL OF ALGORITHMS AND COMPUTATION
Year:2019 | Volume:51 | Issue:2|Papers Count:12

Let G be a graph and f: V (G)! {1, 2, 3, . . . . . |V (G)|} be a bijection. Let puv = f(u)f(v) and duv =        hf(u) f(v) i if f(u)  f(v) hf(v) f(u)i if f(v)  f(u) for all edge uv 2 E(G). For each edge uv assign the label 1 if gcd(puv, duv) = 1 or 0 otherwise. f is called PD-prime cordial labeling if |ef (0) − ef (1)|  1 where ef (0) and ef (1) 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.

In this paper, we design a data structure for the follow-ing problem. Let  be an x-monotone trajectory with n vertices in the plane and  > 0. We show how to preprocess  and  into a data structure such that for any horizontal query segment Q in the plane, one can quickly determine the minimal continuous fraction of  whose Fr echet and Hausdor distance to the horizon-tal query segment Q is at most some threshold value  . We present a data structure for this query that needs O(n log n) preprocessing time, O(n) space, and O(log n) query time.

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  xed dimension d, and propose a new (1 + ")-approximation algorithm with O(n + 1="d􀀀 1) time and O(n) space, where 0 < " 6 1. We also show that the proposed algorithm can be modi ed to a (1 + O("))-approximation algorithm with O(n + 1=" 2d 3 􀀀 1 2 ) running time. Our proposed algorithms are di erent 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.

An outer connected dominating(OCD) set of a graph G = (V; E) is a set ~D  V such that every vertex not in S is adjacent to a vertex in S, and the induced subgraph of G by V n ~D, i. e. G[V n ~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

Suppose G is a simple and connected graph. The  rst and second Zagreb indices of G are two degree-based graph invariants de ned as M1(G) = P v2V (G) deg(v)2 and M2(G) = P e=uv2E(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 jSj = p, G n S is k􀀀 cyclic and there is no a subset S0 of V (G) such that jS0j < jSj and G n S0 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  3.

Analyzing eyes performance is essential for e ective functioning of human. Therefore, following their motion could help doctors to make quick and accurate diagnoses for disorders like Autism, schizophrenia, or attention de cit 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 su cient accurate to appropriate function on videos with varying quality. The direct analysis of gaze and study of

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 (OptMST) problem on S. The 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 L1-metric. We present a ( 3 7)-approximation algorithm for Max-MST. This is an improvement on the best-known approximation factor of 1=3. If S satis es k-separability property (the distance between any pair of squares are at least k: amax where amax is the maximum length of the squares), the factor parameterizes to 2k+3 2k+7. We propose a new lower bound for Min-MST problem on S under L1-metric where S contains unit squares and provide an approximation algorithm with (1 + 2p2) asymptotic factor.

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 e ciency of XOA, algorithms for 30 di erent benchmarks have been analyzed and compared to some novel and renowned metaheuristic algorithms. The simulation response illustrates a significant improvement in

The tenacity of a graph G, T(G), is de ned by T(G) = minfjSj+ (G􀀀 S)! (G􀀀 S) g, where the minimum is taken over all vertex cutsets S of G. We de ne  (G 􀀀 S) to be the number of the vertices in the largest component of the graph G 􀀀 S, and! (G 􀀀 S) be the number of components of G 􀀀 S. In this paper we consider the relationship between the minimum degree  (G) of a graph and the complexity of recognizing if a graph is T-tenacious. Let T  1 be a rational number. We  rst show that if  (G)  Tn T+1, then G is T-tenacious. On the other hand, for any  xed  > 0, we show that it is NP-hard to determine if G is T-tenacious, even for the class of graphs with  (G)  ( T T+1 􀀀  )n.

A data-intensive computing platform, encountered in some grid and cloud computing applications, includes numerous tasks that process, transfer or analysis large data  les. 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  le 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 replace-ment issue which makes a signi cant di erence in the e ciency of replication algorithm. We survey