Let u and v be any two distinct vertices of an undirected graph G, which is k-connected. For 1 w k, a w-container C(u, v) of a k-connected graph G is a set of w-disjoint paths joining u and v. A w-container C(u, v) of G is a w *-container if it contains all the vertices of G. A graph G is w *-connected if there exists a w *-container between any two distinct vertices. Let κ(G) be the connectivity of G. A graph G is super spanning connected if G is i *-connected for 1 i κ(G). In this paper, we prove that the n-dimensional burnt pancake graph Bn is super spanning connected if and only if n ≠ 2.

In this paper, we give an algorithm for the node-to-set disjoint paths problem in a transposition graph. The algorithm is of polynomial order of n for an n-transposition graph. It is based on recursion and divided into two cases according to the distribution of destination nodes. The maximum length of each path and the time complexity of the algorithm are estimated theoretically to be O(n7) and 3n - 5, respectively, and the average performance is evaluated based on computer experiments.

In this paper, we study the layout problem of the supercube by embedding-in-book technique. The supercube, a generalization of the hypercube, can be constructed for an arbitrary system size. Moreover, it has the same diameter and connectivity of the corresponding hypercube. Embedding a graph in book is to place nodes along the spine of the book and to draw the edges such that edges residing in a page do not cross. An n-dimensional hypercube is regular because the degree of each node is n. The corresponding supercube with N nodes, where 2n-1 < N 2n and N ≠ 32n-2, is irregular because the degree of each node ranges from 2n - 2 to n - 1. Although Chung et al. have shown that an n-dimensional hypercube can be embedded with n - 1 pages, to lay out the supercube remains a challenging problem owing to its higher degree and irregular structure. In this paper, we show that a supercube of N nodes, where 2n-1 < N 2n, can also be embedded with n - 1 pages and book width N - 2n-2 for 2n-1 < N < 32n-2, and 2n-1 for 32n-2 N 2n.

This note shows an efficient implementation of de Bruijn networks by the Optical Transpose Interconnection System (OTIS) extending previous results by Coudert, Ferreira, and Perennes [2].

Adaptive routing algorithms, which dynamically select the route of a packet, have been widely studied for interconnection networks in massively parallel computers. An output selection function (OSF), which decides the output channel when some legal channels are free, is essential for an adaptive routing. In this paper, we propose a simple and efficient OSF called minimal multiplexed and least-recently-used (MMLRU). The MMLRU selection function has the following simple strategies for distributing the traffic: 1) each router locally grasps the congestion information by the utilization ratio of its own physical channels; 2) it is divided into the two selection steps, the choice from available physical channels and the choice from available virtual channels. The MMLRU selection function can be used on any type of network topology and adaptive routing algorithm. Simulation results show that the MMLRU selection function improves throughput and latency especially when the number of dimension becomes larger or the number of nodes per dimension become larger.

This paper proposes several novel hierarchical interconnection networks based on the (3, 3)-graphs, namely folded (3, 3)-networks, root-folded (3, 3)-networks, recursively expanded (3, 3)-networks, and flooded (3, 3)-networks. Just as the hypercubes, CCC, Peterson-based networks, and Heawood-based networks, these hierarchical networks have the following nice properties: regular topology, high scalability, and small diameters. Due to these important properties, these hierarchical networks seem to have the potential as alternatives for the future interconnection structures of multicomputer systems, especially massively parallel processors (MPPs). Furthermore, this paper will present the routing and broadcasting algorithms for these proposed networks to demonstrate that these algorithms are as elegant as the algorithms for hypercubes, CCC, and Petersen- or Heawood-based networks.

In this paper, we give an algorithm for the node-to-set disjoint paths problem in pancake graphs with its evaluation results. The algorithm is of polynomial order of n for an n-pancake graph. It is based on recursion and divided into two cases according to the distribution of destination nodes in classes into which all the nodes in a pancake graph are categorized. The sum of lengths of paths obtained and the time complexity of the algorithm are estimated and the average performance is evaluated based on computer simulation.

A minimum feedback node set in a graph is a minimum node subset whose deletion makes the graph acyclic. Its detection in a dependency graph is important to recover from a deadlock configuration. A livelock configuration is also avoidable if a check point is set in each node in the minimum feedback node set. Hence, its detection is very important to establish dependable network systems. In this letter, we give a minimum feedback node set in a trivalent Cayley graph. Assuming that each word has n bits, for any node, we can judge if it is included in the set or not in constant time.

For any pair of distinct nodes in an n-pancake graph, we give an algorithm for construction of n-1 internally disjoint paths connecting the nodes in the time complexity of polynomial order of n. The length of each path obtained and the time complexity of the algorithm are estimated theoretically and verified by computer simulation.

We derive an efficient and simple analytical expression for estimating maximum simultaneous switching noise (SSN) on ground distribution networks in CMOS systems. In order to estimate maximum SSN voltages, we use α-power law MOS model and Taylor's series approximation. The accuracy of the proposed expression is verified by comparing the results with those of previous researches and HSPICE simulations under the contemporary process parameters and environmental conditions. The proposed method predicts the maximum SSN values more accurately when compared to existing approaches even in most practical cases such that there exist some output drivers not in transition.

Many researchers have used hypercube interconnection networks for their good properties to construct many parallel processing systems. However, as the number of processors increases, the probability of occurrences of faulty nodes also increases. Hence, for hypercube interconnection networks which have faulty nodes, several efficient dynamic routing algorithms have been proposed which allow each node to hold status information of its neighbor nodes. In this paper, we propose an improved version of the algorithm proposed by Chiu and Wu by introducing the notion of full reachability. A fully reachable node is a node that can reach all nonfaulty nodes which have Hamming distance l from the node via paths of length l. In addition, we further improve the algorithm by classifying the possibilities of detours with respect to each Hamming distance between current and target nodes. We propose an initialization procedure which makes use of an equivalent condition to perform this classification efficiently. Moreover, we conduct a simulation to measure the improvement ratio and to compare our algorithms with others. The simulation results show that the algorithms are effective when they are applied to low-dimensional hypercube interconnection networks.

In this paper, a new network structure called generalized Hierarchical Completely-Connected networks (HCCs) is proposed, and its properties and features are evaluated. Simple routing strategies for HCCs are also developed for shortest-paths routing algorithms. A set of HCCs constructed by the proposed method includes some conventional hierarchical networks, then it is called generalized one. The construction of an HCC starts from a basic block (a level-1 block) which consists of n nodes of constant degree. Then a level-h block for h 2 is constructed recursively by interconnecting any pair of macro nodes (n level-(h-1) blocks) completely. An HCC has a constant node-degree regardless of an increase in its size (the number of nodes). Furthermore, since an HCC has a hierarchically structured topology and the feature of uniformity, a wide variety of inter-cluster connections is possible. Evaluation results show that an HCC is suitable for very large computer systems.

For a given N-vertex graph H, a graph G obtained from H by adding t vertices and some edges is called a t-FT (t-fault-tolerant) graph for H if even after deleting any t vertices from G, the remaining graph contains H as a subgraph. For the n-dimensional cube Q(n) with N vertices, a t-FT graph with an optimal number O(tN+t2) of added edges and maximum degree of O(N+t), and a t-FT graph with O(tNlog N) added edges and maximum degree of O(tlog N) have been known. In this paper, we introduce some t-FT graphs for Q(n) with an optimal number O(tN+t2) of added edges and small maximum degree. In particular, we show a t-FT graph for Q(n) with 2ctN+ct2((logN)/C)C added edges and maximum degree of O(N/(logC/2N))+4ct.

Advanced scientific and engineering problems require massively parallel computing. Critical to the designand ultimately the performanceof such computing systems is the interconnection network binding the computing elements, just as is the cardiovascular network to the human body. This paper develops a new interconnection network, "Tori connected mESHes (TESH)," consisting of k-ary n-cube connection of supernodes that comprise meshes of lower level nodes. Its key features are the following: it is hierarchical, thus allowing exploitation of computation locality as well as easy expansion (up to a million processors), and it appears to be well suited for 3-D VLSI implementation, for it requires far fewer number of vertical wires than almost all known multi-computer networks. Presented in the paper are the architecture of the new network, node addressing and message routing, 3-D VLSI/ULSI considerations, and application of the network to massively parallel computing. Specifically, we discuss the mapping on to the network of stack filtering, a hardware oriented technique for order statistic image filtering.

This paper first proposes a new approach to designing high-quality, low-diameter, small mean-internode-distance (MID), k-subcubic-connected cyclic networks. The approach is a modification of the k-cubic-connected cyclic (k-ccc) network in which there are N=k2k-1 instead of N=k2k nodes in the k-ccc network. The special features of this network are: (1) It fills the gap between the number of nodes in k-ccc and (k+1)-ccc networks, but retains a constant number of link (3) per node in the network, (2) it allows higher quality, smaller diameters and mean internode distances hypercube networks with the same numbers of nodes. A second novel approach consists of a k+-sccc network with the same number of nodes as the k-ccc but with smaller diameters and mean internode distances. A generalized k-ccc network formed by nodes N=k2m is introduced for n-cube and k-ccc (modified or normal) networks that allows minimum network quality to be obtained where m may or may not equal to k. A routing algorithm for 4-sccc is also presented.

This paper explores the potential of multiwave interconnectionsoptical interconnections that employ wavelength components as multiplexable information carriersfor constructing next-generation multiprocessor systems using MCM technology. A hypercube-based multiprocessor network called the multiwave hypercube (MWHC) is proposed, where multiwave interconnections provide highly-flexible dynamic communication channels among processing elements. A performance analysis shows that the use of multiwavelength optics makes possible the reduction of network complexity on an MCM substrate, while supporting low-latency message routing.

Multipath interconnection networks can support higher bandwidth than those of nonblocking networks by passing multiple packets to the same output simultaneously and these packets are buffered in the output buffer. The delay-throughput performance of the output buffer in multipath networks is closely related to output traffic distribution, packet arrival process at each output link connected to a given output buffer. The output traffic distributions are different according to the various input traffic patterns. Focusing on nonuniform output traffic distributions, this paper develops a new, general analytic model of the output buffer in multipath networks, which enables us to investigate the delay-throughput performance of the output buffer under various input traffic patterns. This paper also introduces Multipath Crossbar network as a representative multipath network which is the base architecture of our analysis. It is shown that the output buffer performances such as packet loss probability and delay improve as nonuniformity of the output traffic distribution becomes larger.

In this paper, we consider the following node-to-set disjoint paths problem: given a node s and a set T = {t1,...,tk} of k nodes in a k-connected graph G, find k node-disjoint paths s ti, 1 i k. We give an O(n2) time algorithm for the node-to-set disjoint paths problem in n-dimensional star graphs Gn which are (n - 1)-connected. The algorithm finds the n - 1 node-disjoint paths of length at most d(Gn) + 1 for n 4,6 and at most d(Gn) + 2 for n = 4,6, where d(Gn) = 3(n-1)/2 is the diameter of Gn. d(Gn) + 1 and d(Gn) + 2 are also the lower bounds on the length of the paths for the above problem in Gn for n 4,6 and n = 4,6, respectively.

This paper discusses a massively parallel interconnection scheme for multithreaded architecture and introduces a new class of direct interconnection networks called the hierarchical Multidimensional Directed Cycles Ensemble (hMDCE). Its suitability for massively parallel systems is discussed. The network is evolved from the Multidimensional Directed Cycles Ensemble (MDCE) network, where each node is substituted by lower-level sub-networks. The new network addresses some serious problems caused by the increasing scale of parallel systems, such as longer latency, limited throughput and high implementation cost. This paper first introduces the MDCE network and then presents and examines in detail the hierarchical MDCE network. Bisection bandwidth of hMDCE is considerably reduced from its ancestor MDCE and the network performs significantly higher throughput and lower latency under some practical implementation constraints. The gate count and delay time of the compiled circuit for the routing function are insignificant. These results reveal that the hMDCE network is an important candidate for massively parallel systems interconnection.

In this paper, we study the following node-to-node and node-to-set routing problems in r-dimensional torus Trn with r 2 and n 4 nodes in each dimension: given at most 2r - 1 faulty nodes and non-faulty nodes s and t in Trn, find a fault-free path s t; and given at most 2r - k faulty nodes and non-faulty nodes s and t1,..., tk in Trn, find k fault-free node-disjoint paths s ti, 1 i k. We give an O(r2) time algorithm which finds a fault-free path s t of length at most d(Trn) + 1 for the node-to-node routing, where d(Trn) is the diameter of Trn. For node-to-set routing, we show an O(r3) time algorithm which finds k fault-free node-disjoint paths s ti, 1 i k, of length at most d(Trn) + 1. The upper bounds on the length of the found paths are optimal. From this, Rabin diameter of Trn is d(Trn) + 1.