Star Graph Interconnection Network Research Articles

The 1-good neighbor connectivity of unidirectional star graph networks

Unidirectional star graphs, the star graph interconnection networks with simplex unidirectional links, can be used in the area of parallel and distributed computing. The 1-good-in-neighbor connectivity, the 1-good-out-neighbor connectivity, and the 1-good-neighbor connectivity are more accurate network reliability indices than the classical connectivity. In this paper, we first give lower bounds on the cardinalities of the out-neighborhood and the in-neighborhood of a vertex subset of a unidirectional star graph and then determine the 1-good-in-neighbor connectivity, the 1-good-out-neighbor connectivity, and the 1-good-neighbor connectivity of unidirectional star graphs.

Analysis of the Minimum and Maximum Numbers of Edges per Each Dimension Required for Constructing a Hamiltonian Cycles in the Star Graph Interconnection Networks

Analysis of the Minimum and Maximum Numbers of Edges per Each Dimension Required for Constructing a Hamiltonian Cycles in the Star Graph Interconnection Networks

Fault-free mutually independent Hamiltonian cycles of faulty star graphs

The star graph interconnection network has been recognized as an attractive alternative to the hypercube for its nice topological properties. Unlike previous research concerning the issue of embedding exactly one Hamiltonian cycle into an injured star network, this paper addresses the maximum number of fault-free mutually independent Hamiltonian cycles in the faulty star network. To be precise, let SG n denote an n-dimensional star network in which f≤n−3 edges may fail accidentally. We show that there exist (n−2−f)-mutually independent Hamiltonian cycles rooted at any vertex in SG n if n∈{3, 4}, and there exist (n−1−f)-mutually independent Hamiltonian cycles rooted at any vertex in SG n if n≥5.

Path embedding in star graphs

The star graph interconnection network has been introduced as an attractive alternative to the hypercube network. In this paper, we consider the path embedding problem in star graphs. Assume that n ⩾ 4 . We prove that paths of all even lengths from d ( x , y ) to n ! - 2 can be embedded between two arbitrary vertices x and y from the same partite set in the n-dimensional star graph. In addition, paths of all odd lengths from d ( x , y ) to n ! - 1 can be embedded between two arbitrary vertices x and y from different partite sets in the n-dimensional star graph except that if x and y are adjacent, there is no path of length 3 between them. The result is optimal in the sense that paths of all possible lengths are found in star graphs.

An Efficient Tree-Based Multicasting Algorithm on Wormhole-Routed Star Graph Interconnection Networks Embedded with Hamiltonian Path

Multicasting is an important issue for numerous applications in parallel and distributed computing. In multicasting, the same message is delivered from a source node to an arbitrary number of destination nodes. The star graph interconnection network has been recognized as an attractive alternative to the popular hypercube network. In this paper, we propose an efficient and deadlock-free tree-based multi-cast routing scheme for wormhole-routed star graph networks with hamiltonian path. In our proposed routing scheme, the router is with the input-buffer-based asynchronous replication mechanism that requires extra hardware cost. Meanwhile, the router simultaneously sends incoming flits on more than one outgoing channel. We perform simulation experiments with the network latency and the network traffic. Experimental results show that the proposed scheme reduces multicast latency more efficiently than other schemes.

Optimal broadcasting on incomplete star graph interconnection networks

Broadcasting is an important collective communication operation in many applications which use parallel computing. In this paper, we focus on designing broadcasting algorithms for general incomplete star graphs. We propose two optimal one-to-all broadcasting algorithms for incomplete star graphs with a single-port communication model. An incomplete star graph with N nodes, where (n - 1)! < N < n!, is a subgraph of an n-dimensional star graph. The first scheme is single-message one-to-all broadcasting that takes O(nlogn) steps. The second one is multi-message one-to-all broadcasting that takes O(nlogn + m) steps.

Multipath-Based Multicasting Strategies for Wormhole-Routed Star Graph Interconnection Networks

The star graph interconnection network has been recognized as an attractive alternative to the popular hypercube network. In this paper, we present a multipath-based multicast routing model for wormholerouted star graph networks, propose two efficient multipath routing schemes, and contrast the performance of the proposed schemes with the performance of the scheme presented in our previous work. Both of the two proposed schemes have been proven to be deadlock-free. The first scheme, simple multipath routing, uses multiple independent paths for concurrent multicasting. The second scheme, two-phase multipath routing, includes two phases: source-to-relay and relay-to-destination. For each phase, multicasting is carried out using simple multipath routing. Experimental results show that, for short and medium messages with small message startup latencies, the proposed schemes reduce multicast latency more efficiently than other schemes.

A dual-hamiltonian-path-based multicasting strategy for wormhole-routed star graph interconnection networks

Multicast is an important collective communication operation on multicomputer systems, in which the same message is delivered from a source node to an arbitrary number of destination nodes. The star graph interconnection network has been recognized as an attractive alternative to the popular hypercube network. In this paper, we first address a dual-hamiltonian-path-based routing model with two virtual channels based on two hamiltonian paths (HPs) and a network partitioning strategy for wormhole-routed star graph networks. Then, we propose three efficient multicast routing schemes on basis of such a model. All of the three proposed schemes are proved deadlock-free. The first scheme, network-selection-based dual-path routing, selects subnetworks that are constructed either by the first HP or by the second HP for dual-path routing. The second one, optimum dual-path routing, selects subnetworks with optimum routing path for dual-path routing. The third scheme, two-phase optimum dual-path routing, includes two phases, source-to-relay and relay-to-destination. Finally, experimental results are given to show that our proposed three routing schemes outperform the unicast-based, the HP, and the single-HP-based dual-path routing schemes significantly.

Multicast communication in wormhole-routed star graph interconnection networks

Multicast, an important communication mechanism, is frequently applied in parallel computing. The star graph interconnection network, when compared with the hypercube network, being with low degree and small diameter, has been recognized to be an attractive alternative to the popular hypercube network. In this paper, we derive a node labeling formula based on a hamiltonian path and propose four efficient multicast routing schemes in wormhole-routed star networks with multidestination routing capability. All of the four proposed schemes are path-based and deadlock-free. The first scheme, dual-path routing, sends the message in parallel through two independent paths (toward high label nodes and low label nodes). The second one, shortcut-node-based dual-path routing, is similar to dual-path routing except that the routing tries to find a shortcut node to route the message as soon as possible to reduce the length of transmission path. The third one, multipath routing, is a multiple dual-path routing strategy that includes source-to-relay and relay-to-destination phases. The last scheme, proximity grouping routing, is similar to multipath routing except that in the partitioning step of source and destination nodes the relation of spatial locality of nodes is also taken into account to reduce the length of transmission paths. Finally, the experimental results are given to show that the performance based on unicast-based and traditional hamiltonian-path routing schemes can be improved significantly by the four proposed routing schemes respectively.

Unicast-based multicast algorithm in wormhole-routed star graph interconnection networks

A contention-free unicast-based multicast algorithm is developed for wormhole-routed star graph interconnection networks. Since the size of the buffers in the wormhole routing controller is much smaller than the size of the message, only destination nodes of multicast should receive message and store it in their local buffers; all other nodes can only relay message via their routing controllers. For this reason, the neighbor-to-neighbor communications approach (used for developing broadcast, scatter and total exchange algorithms) is replaced with a hierarchical approach: a multicast tree composed of unicasts, in which only destination nodes receive the message. Furthermore, a methodology for proving the contention-free property of the hierarchical multicast implementation of the algorithm is developed. This methodology provides sufficient conditions for contention avoidance in the multicast algorithm regardless of the number of simultaneous unicasts permitted by the hardware architecture of the communication processor from the particular node. In order to eliminate contention in the multicast algorithm, a deterministic nonminimal routing algorithm is developed as well. It is shown that the proposed nonminimal routing uses only the same number of virtual channels, ( n−1) required by the minimal routing to avoid deadlock. This feature allows minimal and nonminimal routing to exist in the network at the same time.

Efficient sorting on the star graph interconnection network

Two algorithms for sorting n! numbers on an n-star interconnection network are described. Both algorithms are based on arranging the n! processors of the n-star in a virtual (n - 1)- dimensional array. The first algorithm runs in O(n 3 log n time. This performance matches that of the fastest previously known algorithm for the same problem. In addition to providing a new paradigm for sorting on the n-star, the proposed algorithm has the advantage of being considerably simpler to state while requiring no recursion in its formulation. Its idea is to sort the input by repeatedly sorting the contents of all rows in each dimension of the (n - 1>algorithm presented in this paper is more efficient. It runs in O(n 2) time and thus provides an asymptotic improvement over its predecessors. However, it is more elaborate as it uses an existing result for sorting optimally on an (n-1)-dimensional array.

Fault-tolerant ring embedding in a star graph with both link and node failures

The star graph interconnection network has been recognized as an attractive alternative to the hypercube network. Previously, the star graph has been shown to contain a Hamiltonian cycle. In this paper, we consider an injured star graph with some faulty links and nodes. We show that even with f/sub e//spl les/n-3 faulty links, a Hamiltonian cycle still can be found in an n-star, and that with f/sub v//spl les/n-3 faulty nodes, a ring containing at most 4f/sub v/ nodes less than that in a Hamiltonian cycle can be found (i.e. the ring contains at least n!-4f/sub v/ nodes). In general, in an n-star with f/sub e/ faulty links and f/sub v/ faulty nodes, where f/sub e/+f/sub v//spl les/n-3, our embedding is able to establish a ring containing at least n!-4f/sub v/ nodes.

Computation in faulty stars [hypercube networks

The question of simulating a completely healthy hypercube with a degraded one (one with some faulty processors) has been considered by several authors. We consider the question for the star-graph interconnection network. With suitable assumptions on the fault probability, there is, with high probability, a bounded distance embedding of K/sub n/spl times/S/sub n-1/ in a degraded S/sub n/, of congestion O(n). By a different method, a congestion O(log(n)) embedding of S, can be obtained. For the hypercube O(1) congestion has been obtained, but this is open for the star graph. Other results presented include a guaranteed O(n) slowdown simulation if there are sufficiently few faults, and upper and lower bounds for the minimal size of a system of faults rendering faulty every m-substar.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Routing Function and Deadlock Avoidance in a Star Graph Interconnection Network

In this paper the properties of paths in a star graph are investigated through the analysis of the corresponding star transposition tree. The general algebraic expression for all shortest paths between any two nodes (routing function) is found, and it is shown that every shortest path consists of a number of subpaths which can be combined in an arbitrary order or even mutually nested. Further, due to the known routing function the deadlock problem is solved using the method of virtual channels. A minimal deterministic routing algorithm is developed which recognizes the structure of the path by extracting subpaths and allows optimal adaptive management of virtual channels. Finally, based on the sufficient number of virtual channels, the minimal fully adaptive routing algorithm is suggested which offers an opportunity to reroute the message a number of times, while maintaining the shortest path between two nodes.

Communication aspects of the star graph interconnection network

Basic communication algorithms for star graph interconnection networks are developed by using the hierarchical properties of the star graph, with the assumption that one input channel can drive only one output communication channel at a time. With this constraint, communication algorithms for each node can be expressed only as sequences of generators corresponding to the communication channels. Sequences that are identical exploit the symmetry and hierarchical properties of the star graph and can be easily integrated in communication hardware. Their time complexities are evaluated and compared with the corresponding results for the hypercube.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Fault tolerance of the star graph interconnection network

This paper computes the exact fault diameter of the star graph. The fault diameter of a graph is the maximum diameter achievable, when we delete from the original graph any set of nodes that is smaller than its vertex connectivity. We show that for S 3 and S 4 the exact fault diameter is the original diameter plus two, and for S n , n>4, the fault diameter is the original diameter plus one.

A broadcasting algorithm in star graph interconnection networks

A broadcasting algorithm in star graph interconnection networks