Cluster model for optimal double-loop connected network

The authors introduce and study a family of interconnection schemes, the Midimew networks, based on circulant graphs of degree 4. A family of such circulants is determined and shown to be optimal with respect to two distance parameters simultaneously, namely maximum distance and average distance, among all circulants of degree 4.. These graphs are regular, point-symmetric, and maximally connected, and one such optimal graph exists for any given number of nodes. The proposed interconnection schemes consist of mesh-connected networks with wrap-around links, and are isomorphic to the optimal distance circulants previously considered. Ways to construct one such network for any number of nodes are shown, their good properties to build interconnection schemes for multicomputers are examined, and some interesting particular cases are discussed. The problem of routing is also addressed, and a basic algorithm is provided which is adequate for implementing the routing policy required to convey messages, traversing shortest paths between nodes.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

We propose a new family of interconnection topology that can be used to design communication architecture for distributed systems with an arbitrary number of computing nodes. The design is based on a novel generalization of the well known hypercube graphs. The proposed topology is shown to be incrementally extensible in steps of 1 (cost of restructuring or adding edges is very low), optimally fault tolerant and its diameter is logarithmic in the number of nodes. Moreover, for any given number of nodes, the difference of the maximum and the minimum degree of a node in the graph is ≤1, i.e., the graph is almost regular. A shortest routing algorithm for the proposed family of graphs has been developed.

Interconnection Networks are widely used in many applications such as parallel and massively parallel systems, industrial applications, VLSI circuits, electronic devices and telephone switches etc. The realization of data communication in parallel system is possible all the way through interconnection networks. The whole performance of the system depends on the type of interconnection networks used. Interconnection networks with embed ability by some other interconnection structure, high resilience, simple routing, constant node degree, and scalability are highly desirable. We had introduced Octagon-Cell Networks (OCN), in the past research, which is a new interconnection network. In this research, we introduce and prove the fundamental theorems for finding the optimal path length between any pair of source and destination nodes in Octagon-Cell Network of any depth. The basic objective of these theorems (excluding Horizontal and Vertical Moves) to calculate the optimal path length, is to check whether any intermediate node exists along the optimal path, for which its line number or serial number matches with the line number or the serial number of destination node respectively. We also introduce the theorems to find the total number of horizontal lines, which is the maximum line number of a node, as well the total number of vertical lines, which is the maximum serial number of a node in Octagon-Cell Network of any depth. The theorems are proved mathematically and are tested successfully on all possible cases.

The capacitated family traveling salesperson problem (CFTSP) is about a graph in which nodes are partitioned into disjoint and differently weighted families. The objective is to find the shortest route that visits a given number of nodes in each family with a set of capacitated agents. The CFTSP is a new variant of the family traveling salesman problem (FTSP). Nevertheless, existing exact and metaheuristic methods for the FSTP cannot be straightforwardly applied due to the feasibility condition that requires agents to stay within their capacity. Thus, we propose integer linear programming formulations with five different subtour inequalities sets that are tested and compared with the classical approaches. In addition, we propose a biased random‐key genetic algorithm with four decoder algorithms that find high‐quality solutions in short computational times. Based on our experiments, we have found that our methods are effective in addressing subtour avoidance and ensuring feasible assignments.

Extension of synchronizability analysis based on vital factors: Extending validity to multilayer fully coupled networks

In this article for a finite typed random geometric graph we define the\nempirical locality distribution, which records the number of nodes of a given\ntype linked to a given number of nodes of each type. We find large deviation\nprinciple (LDP) for the empirical locality measure given the empirical pair\nmeasure and the empirical type measure of the typed random geometric graphs.\nFrom this LDP, we derive large deviation principles for the degree measure and\nthe proportion of detached nodes in the classical Erdos-Renyi graph defined on\n[0, 1]^d. This graphs have been suggested by (Canning and Penman, 2003) as a\npossible extension to the randomly typed random graphs.\n

A pancake graph was proposed as a topology for interconnection networks of parallel computers, and it has a merit that it can connect many nodes with small diameter and small degree. However, the number of nodes in a pancake graph must be equal to the factorial of an integer, which causes a demerit that it lacks incremental expandability. Hence, in this paper, we propose a graph, an incomplete pancake graph, that is obtained by deleting some of sub graphs of a pancake graph, and we give algorithms for the problems of the simple routing, the Hamiltonian cycle, the Hamiltonian path, and the container in incomplete pancake graphs.

Development of a computationally-tractable design method for combined multi-physics optimization of packing and routing problems, at a relevant scale, within compact packaging volumes, will offer benefits across several engineering domains. But for performing multi-physics packing and routing optimization, the generation of spatially feasible initial layouts is essential. Three new and computationally efficient methods are demonstrated in this article to produce automatically interference-free 2D geometric layouts. First, a novel 2D force-directed layout method (FDLM) is proposed that implicitly ensures noninterference between components and/or the interconnect network by utilizing spring force theory without using explicit geometric constraints. Second, the A* algorithm, a well-established 2D shortest path algorithm (SPA), has been modified significantly to perform efficient routing of complex interconnect systems. Third, a new geometric topology (GT) enumeration algorithm is presented that produces all unique interconnect routing configurations for given multi-component system architecture. These layout generation methods are then compared with respect to average computational efficiencies and average success rates in attaining feasible layouts for a restricted class of topologies, including evaluation of how the methods scale to problems with an increased number of components. Limitations and future work items for each method are discussed. These methods are presented as an important step toward solution strategies that are compatible with the currently unmet challenges of real-world 2D and 3D combined packing and routing problems, including efficient navigation of the space of discrete options for interconnect geometric topology, as well as scaling to more complex problems.

Hierarchical hypercubes (HHC), also known as cube-connected cubes, have been introduced in the literature as an interconnection network for massively parallel systems. Effectively, they can connect a large number of nodes while retaining a small diameter and a low degree compared to a hypercube of the same size. Especially (2 m +m)-dimensional hierarchical hypercubes ( $\mathit {HHC}_{2^{m}+m}$ ), called perfect HHCs, are popular as they are symmetrical, which is a critical property when designing routing algorithms. In this paper, we describe an algorithm finding, in an $\mathit{HHC}_{2^{m}+m}$ , mutually node-disjoint paths connecting k=?(m+1)/2? pairs of distinct nodes. This problem is known as the k-pairwise disjoint-path routing problem and is one of the important routing problems when dealing with interconnection networks. In an $\mathit{HHC}_{2^{m}+m}$ , our algorithm finds paths of lengths at most 2 m+1+m(2 m+1+1)+4 in O(25m ) time, where 2 m+1 is the diameter of an $\mathit{HHC}_{2^{m}+m}$ . Also, we have shown through an experiment that, in practice, the lengths of the generated paths are significantly lower than the worst-case theoretical estimations.

Supercomputers are today made up of hundreds of thousands of nodes. The interconnection network is responsible for connecting all these nodes to each other. Different interconnection networks have been proposed; high performance topologies have been introduced as a replacement for the conventional topologies of recent decades. A high order, a low degree and a small diameter are the usual properties aimed for by such topologies. However, this is not sufficient to lead to actual hardware implementations. Network scalability and topology simplicity are two critical parameters, and they are two of the reasons why modern supercomputers are often based on torus interconnection networks (e.g., Fujitsu K, IBM Sequoia). In this paper we first describe a new topology, torus-connected cycles (TCCs), realizing a combination of a torus and a ring, thus retaining interesting properties of torus networks in addition to those of hierarchical interconnection networks (HINs). Then, we formally establish the diameter of a TCC, and deduce a point-to-point routing algorithm. Next, we propose routing algorithms solving the Hamiltonian cycle problem, and, in a two dimensional TCC, the Hamiltonian path one. Correctness and complexities are formally proved. The proposed algorithms are time-optimal.

We recently proposed a new algorithm which routes a class of 2log/sub 2/N- or (2log/sub 2/N-1)-stage rearrangeable networks. Although we discussed some of the general rules for proper routing, detailed strategies for resolving possible conflicts were not mentioned. In this paper, we point out additional conditions which enable conflict-free routing in the original algorithm. Cyclic property at the center stages is analyzed in more detail. We also show that the routing problem in the concatenation of two omega networks known as 2log/sub 2/N-stage shuffle network, is in the class of NP-completeness.

Controlling the dynamics of biological neuronal network (BNNs) is of great importance for both understanding the brain and for developing means to control brain disease related aberrant activity. In the last decade, the relationship among node properties, network structure and network dynamics has become clearer and several neuron and network properties could be used to control the network dynamics. Designing appropriate control inputs would require selective manipulation of the control variable in each node. However, the large size of BNNs and scarcity of resources do not allow control of all individual nodes by external means. Therefore, there is a need to identify a much smaller number of influential nodes that are sufficient to drive the activity dynamics of the entire BNN to a desired state. Here, we used the concept of structural controllability [1] to identify a small set of influential nodes, control nodes, for synthetic and experimental networks. The later includes large-scale connectivity of macaque cortical regions [2], meso-scale connectome of a mouse brain [3] and the neuronal connectivity of C. elegans [4]. We investigated the effect of random and systematic edge pruning on the number of these control nodes. Moreover, We showed that there is a power law or exponential dependence between the number of control nodes and the average degree of many networks. Finally, we used a simplified network of the basal ganglia to qualitatively show that few control nodes can indeed drive the network dynamics to a desired state. While every sub-network could be used as a control node or sensor, each node is different in terms of the required stimulation pattern, stimulation energy and time to reach the desired dynamical state.

We present a family of interconnection networks named the Cube-Of-Rings (COR) networks along with their basic graph-theoretic properties. Aspects of group graph theory are used to show the COR networks are symmetric and optimally fault tolerant. We present a closed-form expression of the diameter and optimal one-to-one routing algorithm for any member of the COR family. We also discuss the suitability of the COR networks as the interconnection network of scalable parallel computers.

This article introduces methods for initializing a single-trajectory-based metaheuristic, specifically a simulated annealing (SA) algorithm, using constructive heuristics. These methods are designed to target promising regions within the search space of an nondeterministic polynomial time (NP)-hard problem, namely the single allocation p-hub center and routing problem. The objective of this problem is to allocate demand centers to hubs and design vehicle routes such that the maximum distance between all origin-destination pairs is minimized. To analyze the impact of different initial solutions, various constructive heuristics, including greedy and hybrid strategies, have been proposed. Additionally, a problem decomposition approach leveraging domain-specific knowledge has been incorporated through a matheuristic initial solution strategy to enhance the efficiency of the simulated annealing algorithm. This approach generates high-quality initial solutions by first solving the p-hub center problem and then using the obtained hubs and their assignments as inputs to the min-max multiple traveling salesman problem. In this problem, the objective function is formulated differently from the literature by minimizing the longest distance between the two nodes. Several experiments have been conducted on the Turkish network, and upon examining the results, it has been observed that each initial solution generation strategy provides improvements in problem instances with specific characteristics, such as the number of vehicles and nodes. We also observed lower objective function values for all medium- and large-sized test problems taken from the literature, highlighting the effectiveness of the proposed strategies.

we study the problem of transmission-side diversityand routing in a static wireless network. In this paper, we present a new medium access control (MAC) protocol forad-hoc networks with multiple input multiple output (MIMO) links. Instead of using perfect synchronizationtechnique, we assume the cooperative transmission is asynchronous. It is shown that the energy savings of 39% and 56% areachievable in line and grid networks with a large number of nodes, respectively.This paper describes theassumptions, the implementation process and the challenges wewere presented with.The MAC protocol proposed in addresses thisissue using an efficient cooperative scheme. Ageneral decision feedback equalizer (DFE) is used in the receiving cluster members to equalize the received MISO signal and detect as soft symbols. The receiving cluster members send the soft decision outputs to the destination node.Up to 80% in energysavings can be achieved for a grid topology, while for random nodeplacement our cooperative protocol can save up to 40% in energyconsumption relative to the other protocols.