Optical Transpose Interconnection System Research Articles

A comparison between certain graph parameters of biswapped networks and their maximal twin-preserving subgraphs with applications in determining complexity

The study of different objects, such as the properties of algebraic structures, the analysis of chemical graph structures without experiment, and understanding networks through topological indices (TIs), is among the modern directions in graph theory. The analysis of different networks, such as the Benes network, butterfly network, hex-derived network and biswapped network, using TIs is one of the modern research fields. The storage and transfer of data carrying certain information has always remained a modern world problem. The optoelectronic technology used in optical transpose interconnection systems (OTIS) is efficient in outcome over an electrical system due to the minimum power consumption and broad bandwidth. By combining the use of wireless and electrical technologies, OTIS has developed into a valuable network and boosted the efficiency of contemporary optoelectronic computers. A special type of OTIS is the biswapped network over the path graph Pn , denoted by . In this article, a maximal twin-preserving subgraph of a biswapped network over the path graph Pn is constructed. Moreover, the biswapped network and its constructed subgraph are compared through ev-degree- and ve-degree-dependent TIs. In addition to this, to analyse the complexity of and through information functional-based entropies, we define ve-degree- and ev-degree-based information functionals and compute formulae for ve-degree- and ev-degree-based entropies. The analytical formulae, tables and graphical trends are used to describe a comparison between the TIs and entropies of and . It is shown that the values of TIs and entropies only differ by a constant depending on the value of n.

Fault-Tolerant Resolvability of Swapped Optical Transpose Interconnection System

Interconnection systems in computer science and information technology are mainly represented by graphs. One such instance is of swapped network simulated by the optical transpose interconnection system (OTIS). Fault tolerance has become a vital feature of optoelectronic systems. Among multiple types of faults that may take place in an interconnection system, two significant kinds are either due to malfunctioning of a node (processor in case of O G ) or collapse of communication between nodes (failure of interprocessor transmission). To prevail over these faults, the unique recognition of every node is essential. In graph-theoretic interpretation, this leads to instigating the metric dimension β O G and fault-metric dimension β ′ O G of the graph O G obtained from the interconnection system. This paper explores OTIS over base graph P m (path graph over m vertices) for resolvability and fault-tolerant resolvability. Furthermore, bounds for β O G and β ′ O G are also imparted over G = P m .

Petersen-star networks modeled by optical transpose interconnection system

One method to create a high-performance computer is to use parallel processing to connect multiple computers. The structure of the parallel processing system is represented as an interconnection network. Traditionally, the communication links that connect the nodes in the interconnection network use electricity. With the advent of optical communication, however, optical transpose interconnection system networks have emerged, which combine the advantages of electronic communication and optical communication. Optical transpose interconnection system networks use electronic communication for relatively short distances and optical communication for long distances. Regardless of whether the interconnection network uses electronic communication or optical communication, network cost is an important factor among the various measures used for the evaluation of networks. In this article, we first propose a novel optical transpose interconnection system–Petersen-star network with a small network cost and analyze its basic topological properties. Optical transpose interconnection system–Petersen-star network is an undirected graph where the factor graph is Petersen-star network. OTIS–PSN n has the number of nodes 102n, degree n+3, and diameter 6 n − 1. Second, we compare the network cost between optical transpose interconnection system–Petersen-star network and other optical transpose interconnection system networks. Finally, we propose a routing algorithm with a time complexity of 6 n − 1 and a one-to-all broadcasting algorithm with a time complexity of 2 n − 1.

ON VE-DEGREE AND EV-DEGREE BASED TOPOLOGICAL INDICES OF CERTAIN OTIS BISWAPPED NETWORK

The optical transpose interconnection system (OTIS) arrange has numerous application in designed for equal just as in conveyed arrange. Distinctive interconnection networks has contemplated identified with topological descriptors in [\cite{25,26}]. The present article is a contribution to Ve-degree and Ev-degree base topological indices of biswapped network with premise diagram as path and complete graph. In addition, some delicated recipes are too gotten for various kinds of topological records for the OTIS biswapped network by taking the path and complete graph on $n$ vertices as premise of diagram.

Molecular descriptors of certain OTIS interconnection networks

Network theory as an important role in the field of electronic and electrical engineering, for example, in signal processing, networking, communication theory, etc. The branch of mathematics known as Graph theory found remarkable applications in this area of study. A topological index (TI) is a real number attached with graph networks and correlates the chemical networks with many physical and chemical properties and chemical reactivity. The Optical Transpose Interconnection System (OTIS) network has received considerable attention in recent years and has a special place among real world architectures for parallel and distributed systems. In this report, we compute redefined first, second and third Zagreb indices of OTIS swapped and OTIS biswapped networks. We also compute some Zagreb polynomials of understudy Networks.

Parallel quicksort algorithm on OTIS hyper hexa-cell optoelectronic architecture

In the last two decades, widespread attention has been paid in parallelizing algorithms, such as sorting and searching, for computationally intensive applications. Several interconnection networks were demonstrated for that purpose; such as hypercube and Hyper Hexa-Cell (HHC). However, the leverage of optical links in Optical Transpose Interconnection Systems (OTIS) stimulates the researchers toward developing optoelectronic architectures that utilize the optical links in addition to the electronic links; such as, OTIS-hypercube and OTIS-HHC. In this paper, we introduced a parallel quicksort algorithm for the OTIS-HHC optoelectronic architecture. This algorithm has been evaluated analytically and by simulation in terms of run time, speedup, and efficiency, where a set of simulation runs were carried out on different input data distributions types with various sizes. Thus, simulation results supported the analytical evaluation and met the expectations in which they showed good performance in terms of speedup and efficiency.

Polynomials of Degree-Based Indices for Swapped Networks Modeled by Optical Transpose Interconnection System

The Optical Transpose Interconnection System (OTIS) has applications in parallel processing, distributed processing, routing, and networks. It is used for efficient usage of multiple parallel algorithms or parallel systems, with different global interconnections in a network as it is an optoelectronic (combination of light signals and electronics). In chemical graph theory, topological indices are used to study characteristics of the chemical structures or biological activities. Topological indices are sometimes studied with the assistance to their polynomial. In this article, polynomials of degree-based topological indices for OTIS and swapped networks have been studied. Results can be used to compute any degree-based topological polynomials for OTIS swapped network.

On Topological Indices for Swapped Networks Modeled by Optical Transpose Interconnection System

The optical transpose interconnection system (OTIS) network has many application in architecture for parallel as well as in distributed network. The optical translate interconnection system utilizes a straightforward pair of lenslet clusters to execute a coordinated interconnection that is valuable for mix based multistage interconnection networks, work of-trees network processors, and hypercubes. In Cancan (2019) and Hayat et al. (2014), different interconnection network has studied related to topological indices. In this article we have computed the Ve-degree and Ev-degree base topological indices of swapped network by taking path and complete graph as original graphs. We have included some dedicated formulas for different types of topological indices for the OTIS swapped network by taking the path and complete graph on n vertices as basis of graph.

Calculating topological indices of certain OTIS interconnection networks

AbstractRecently, increasing attention has been paid to The Optical Transpose Interconnection System (OTIS) network because of its prospective applications in architectures for parallel as well as distributed systems [27, 28]. Different interconnection networks in the context of topological indices are researched recently in [25, 26]. This article includes the computions of the general Randi´c, first and second Zagreb, general sum connectivity, first and second multiple zagreb, hyper zagreb, ABC and GA indices for OTIS (swapped and biswapped) networks by taking path and k-regular graph on n vertices as a base graphs. In addition, some delicated formulas are also obtained for the ABC4 and GA5 indices for the OTIS biswapped networks by considering basis graph as a path and k-regular graph of order n.

Parallel heuristic local search algorithm on OTIS hyper hexa-cell and OTIS mesh of trees optoelectronic architectures

Heuristic local search algorithms have achieved good results in tackling combinatorial optimization problems, such as Travelling Salesman Problem (TSP). One of the well-known local search algorithms is the 2-opt algorithm. As a local search algorithm, 2-opt has achieved approximate optimal solutions for TSP within a reasonable time, especially for small data instances. However, solving large data instances of TSP using 2-opt requires extensive computation and considerable CPU time. Therefore, this paper presents a parallel version of the 2-opt algorithm, exploiting the features of Optical Transpose Interconnection System (OTIS) in solving the TSP. In this paper, we present the Parallel Repetitive 2-Opt (PRTO) algorithm for solving symmetric TSP on OTIS Hyper Hexa-Cell (OTIS-HHC) and OTIS Mesh of Trees (OTIS-MOT) optoelectronic architectures. We assess the performance of our algorithm analytically in terms of parallel time complexity, speedup, efficiency, cost, and communication cost on both optoelectronic architectures. Furthermore, a set of simulation experiments is conducted on various instances from the standard TSP library. The simulation results confirm that our algorithm is efficient regarding speedup and efficiency. For instance, the PRTO algorithm achieves a speedup of 32.9 for 6880 cities over OTIS-HHC with 36 processors. Moreover, the superiority of PRTO algorithm is shown through solving the TSP on OTIS-HHC and OTIS-MOT; its performance has been compared with the performance of the Parallel Repetitive Nearest Neighbor (PRNN) algorithm in terms of speedup, efficiency, and solution quality. For example, as a best case, the PRTO algorithm has shown 34 times improved speedup over the PRNN algorithm.

Solving traveling salesman problem using parallel repetitive nearest neighbor algorithm on OTIS-Hypercube and OTIS-Mesh optoelectronic architectures

Over the past years, researchers drew their attention to propose optoelectronic architectures, including optical transpose interconnection system (OTIS) networks. On the other hand, there are limited attempts devoted to design parallel algorithms for applications that could be mapped on such optoelectronic architectures. Thus, exploiting the attractive features of OTIS networks and investigating their performance in solving combinatorial optimization problems become a great necessity. In this paper, a parallel repetitive nearest neighbor algorithm for solving the symmetric traveling salesman problem on OTIS-Hypercube and OTIS-Mesh optoelectronic architectures is presented. This algorithm has been evaluated analytically and by simulation on both optoelectronic architectures in terms of number of communication steps, parallel run time, speedup, efficiency, cost and communication cost. The simulation results attained almost near-linear speedup and high efficiency among the two selected optoelectronic architectures, where OTIS-Hypercube gained better results in comparison with OTIS-Mesh.

Diagnosable evaluation of enhanced optical transpose interconnection system networks

The process of identifying faulty processors is called diagnosis of the system. Several models of diagnosis have been proposed, the most popular being the PMC (Preparata, Metze and Chien) diagnostic model proposed by Preparata et al. in 1967. The precise strategy correctly identifies all faulty processors while the pessimistic strategy isolates all faulty processors within a set containing at most one fault-free processor. For a multiprocessor system, diagnosability is critical to measure its performance. The enhanced optical transpose interconnection system (enhanced OTIS), network has important applications in parallel processing. In this network architecture, n2 processors are divided into n groups of n processors; processors in the same group are connected by electronic links while the groups are simultaneously connected by optical links. An enhanced OTIS network is regular if its base graph G is regular. In this paper, we discuss fault diagnosis in an enhanced OTIS network, including both the precise strategy and pessimistic strategy under the PMC diagnostic model.

Factor‐Optical‐Factor Exchanges Method: a new load balancing method for Extended Optical Transpose Interconnection System‐n‐Cube networks

SummaryThe Optical Transpose Interconnection System (OTIS) optoelectronic interconnection network architecture is a promising attraction in the new era of parallel computing topologies because of its attractive topological properties. Recently, many enhancements were presented on OTIS topologies including the Extended OTIS‐n‐Cube interconnection networks. Therefore, all performance improvement characteristics of such a promising architecture need to be investigated; one of which is load balancing technique. This paper focuses on developing an efficient algorithm for load balancing on the promising Extended OTIS‐n‐Cube interconnection networks. The proposed algorithm is called Factor‐Optical‐Factor Exchange Model. Furthermore, this paper presents theoretical and experimental study on the proposed algorithm in terms of various parameters including execution time, load balancing accuracy, number of communication steps, and speed. Results show superiority of the proposed algorithm over the well‐known Clustered Dimension Exchange Method (CDEM) algorithm in terms of execution time, number of communication steps, and speed, while maintaining the same level of accuracy. Copyright © 2015 John Wiley & Sons, Ltd.

NEARLY OPTIMAL NODE-TO-SET PARALLEL ROUTING IN OTIS NETWORKS

The node-to-set parallel routing problem for a k-connected network Γ is as follows: given a node s and k other nodes {t1, t2, … , tk} in Γ, find k node-disjoint paths connecting s and ti, for 1 ≤ i ≤ k. From the viewpoint of applications in synthesizing fast and resilient collective communication operations, it is desirable to make the parallel paths as short as possible. Building such paths is a nontrivial problem for a general network. Optical transpose interconnection system (OTIS, also known as swapped) networks, a class of hierarchical structures built of n identical n-node factor networks, are known to be maximally fault-tolerant for any connected factor network, implying that they have maximal connectivity. We propose a general algorithm for the node-to-set parallel routing problem in OTIS/swapped networks that yields paths of length no greater than D + 4 in O(Δ2 + Δf(n)) time, where D and Δ represent the diameter and degree of the OTIS network and O(f(n)) is the time complexity of a shortest-path routing algorithm for the n-node factor network. Our node-to-set routing algorithm is shown to have optimal time complexity for certain OTIS networks of practical interest, including OTIS-Mesh and OTIS-Hypercube.

The Optical Chained-Cubic Tree interconnection network: Topological structure and properties

Interconnection networks with optical communication links outperform others using electronic communication links when the distance is long in terms of speed and power consumption. However, for short distances, electronic network topologies are preferred due to lower material cost requirements. As a result, hybrid network topologies were constructed to combine the benefits of both types of network topologies, such as Optical Transpose Interconnection System (OTIS). This paper presents a new hybrid interconnection network topology, which is constructed using both optical and electronic links, called the Optical Chained-Cubic Tree (OCCT). This new OCCT topology is based on the Chained-Cubic Tree (CCT) interconnection network and is designed to cope with both types of binary trees; full and complete. Also, the topological properties of OCCT in terms of diameter, connectivity, degree, bisection width, and cost are presented and compared with OTIS-Mesh and CCT interconnection networks.

The OTIS hyper hexa-cell optoelectronic architecture

Optical transpose interconnection system (OTIS) is an optoelectronic architecture that promises to be a great choice for future-generation parallel systems. OTIS combines the advantages of electronic and optical links, where electronic links are used for short distances which require low material cost, and optical links are used for long distances which provide high speed network with low power consumption. Taking into account the advantageous characteristics of OTIS and based on the attractive properties of hyper hexa-cell (HHC) interconnection topology from low diameter and good minimum node degree, this paper introduces a new optoelectronic architecture referred to as OTIS hyper hexa-cell (OHHC). This paper also provides an evaluation and a comparison of the new topology with OTIS-mesh in terms of the following topological properties: size, diameter, maximum and minimum node degree, bisection width, total cost and optical cost. The results of this study proved the excellence of the proposed OHHC over OTIS-mesh in terms of diameter, minimum node degree, bisection width, and optical cost.

Biswapped networks: a family of interconnection architectures with advantages over swapped or OTIS networks

We propose a new family of communication architectures called ‘biswapped networks’. Given any n-node basis network Ω, the associated biswapped network Bsw(Ω) is built of 2n copies of Ω, using a simple rule for connectivity that ensures desirable attributes, including regularity, modularity, fault tolerance, and algorithmic efficiency. In particular, if Ω is a Cayley digraph, then so is Bsw(Ω). Our biswapped connectivity provides a systematic scheme for synthesizing large, scalable, modular, and robust parallel architectures. Furthermore, many desirable attributes of the underlying basis network Ω are preserved, as the Bsw(Ω) parameters are related to the corresponding parameters of Ω. We obtain a number of results on internode distances, Hamiltonian cycles, optimal routing, and node-disjoint paths for Bsw(Ω). We explore the relations between biswapped and swapped or optical transpose interconnection system (OTIS) networks, which may use a mix of electronic and optical links. In particular, we demonstrate that the biswapped connectivity removes an inherent asymmetry of swapped/OTIS networks, as well as the attendant complications in analyses and applications. Finally, we show that biswapped networks are complementary to, and offer advantages over, well-known and widely used interconnection architectures for parallel processing.

Structural Outlooks for the OTIS-Arrangement Network

Recent studies have revealed that the Optical Transpose Interconnection Systems (OTIS) are promising candidates for future high-performance parallel computers. This paper presents and evaluates a general method for algorithm development on the OTIS-Arrangement network (OTIS-AN) as an example of OTIS network. The proposed method can be used and customized for any other OTIS network. Furthermore, it allows efficient mapping of a wide class of algorithms into the OTIS-AN. This method is based on grids and pipelines as popular structures that support a vast body of parallel applications including linear algebra, divide-and-conquer types of algorithms, sorting, and FFT computation. This study confirms the viability of the OTIS-AN as an attractive alternative for large-scale parallel architectures.

A Multipath Analysis of Biswapped Networks

Biswapped networks of the form Bsw(G) have recently been proposed as interconnection networks to be implemented as optical transpose interconnection systems. We provide a systematic construction of κ+1 vertex-disjoint paths joining any two distinct vertices in Bsw(G), where κ≥1 is the connectivity of G. In doing so, we obtain an upper bound of max{2Δ(G)+5, Δκ(G)+Δ(G)+2} on the (κ+1)-diameter of Bsw(G), where Δ(G) is the diameter of G and Δκ(G) the κ-diameter. Suppose that we have a deterministic multipath source routing algorithm in an interconnection network G that finds κ mutually vertex-disjoint paths in G joining any two distinct vertices and does this in time polynomial in Δκ(G), Δ(G) and κ (and independently of the number of vertices of G). Our constructions yield an analogous deterministic multipath source routing algorithm in the interconnection network Bsw(G) that finds κ+1 mutually vertex-disjoint paths joining any two distinct vertices in Bsw(G) so that these paths, all have length bounded as above. Moreover, our algorithm has time complexity polynomial in Δκ(G), Δ(G) and κ. We also show that if G is Hamiltonian, then Bsw (G) is Hamiltonian, and that if G is a Cayley graph, then Bsw(G) is a Cayley graph.

OTIS-MOT: an efficient interconnection network for parallel processing

Mesh of trees (MOT) is well known for its small diameter, high bisection width, simple decomposability and area universality. On the other hand, OTIS (Optical Transpose Interconnection System) provides an efficient optoelectronic model for massively parallel processing system. In this paper, we present OTIS-MOT as a competent candidate for a two-tier architecture that can take the advantages of both the OTIS and the MOT. We show that an $n^{4}_{-}$ processor OTIS-MOT has diameter 8log?n ?+1 (The base of the logarithm is assumed to be 2 throughout this paper.) and fault diameter 8log?n+2 under single node failure. We establish other topological properties such as bisection width, multiple paths and the modularity. We show that many communication as well as application algorithms can run on this network in comparable time or even faster than other similar tree-based two-tier architectures. The communication algorithms including row/column-group broadcast and one-to-all broadcast are shown to require O(log?n) time, multicast in O(n 2log?n) time and the bit-reverse permutation in O(n) time. Many parallel algorithms for various problems such as finding polynomial zeros, sales forecasting, matrix-vector multiplication and the DFT computation are proposed to map in O(log?n) time. Sorting and prefix computation are also shown to run in O(log?n) time.