Rong-Jaye Chen

The ( n,k )-star graph: a generalized star graph

The objective of this paper is to propose a new topology, called the (n,k)-star graph, such that it removes the restriction of the number of nodes n! in the n-star graph, and preserves many attractive properties of the n-star graph, such as node symmetry, hierarchical structure, maximal fault tolerance and simple shortest routing.

Distance-preserving mappings from binary vectors to permutations

Mappings of the set of binary vectors of a fixed length to the set of permutations of the same length are useful for the construction of permutation codes. In this article, several explicit constructions of such mappings preserving or increasing the Hamming distance are given. Some applications are given to illustrate the usefulness of the construction. In particular, a new lower bound on the maximal size of permutation arrays (PAs) is given.

On the arrangement graph

Abstract The arrangement graph was proposed as a generalization of the star graph topology. In this paper we investigate the topological properties of the (n, k)-arrangement graph An,k. It has been shown that the (n, n − 2)-arrangement graph An,n − 2 is isomorphic to the n-alternating group graph AGn. In addition, the exact value of average distance of An,k has been derived.

TOPOLOGICAL PROPERTIES OF THE (n,k)-STAR GRAPH

The star graph, though an attractive alternative to the hypercube, has a major drawback in that the number of nodes for an n-star graph must be n!, and thus considerably limits the choice of the number of nodes in the graph. In order to alleviate this drawback, the arrangement graph was recently proposed as a generalization of the star graph topology. The arrangement graph provides more flexibility than the star graph in choosing the number of nodes, but the degree of the resulting network may be very high. To overcome that disadvantage, this paper presents another generalization of the star graph, called the (n,k)-star graph. We examine some topological properties of the (n,k)-star graph from the graph-theory point of view. It is shown that two different types of edges in the (n,k)-star prevent it from being edge-symmetric, but edges in each class are essentially symmetric with respect to each other. Also, the diameter and the exact average distance of the (n,k)-star graph are derived. In addition, the fault-diameter for the (n,k)-star graph is shown to be at most the fault-free diameter plus three.

A fast reliability-algorithm for the circular consecutive-weighted-k-out-of-n:F system

An O(T n) algorithm is presented for the circular consecutive-weighted-k-out-of-n:F system, where T/spl les/min[n,[(k-/spl omega//sub max/)//spl omega//sub min/]+1]; /spl omega//sub max/, /spl omega//sub min/ are the maximum, minimum weights of all components. This algorithm is simpler and more efficient than the Wu and Chen O(min[n,k] n) algorithm. When all weights are unity, this algorithm is simpler than other O(k-n) published algorithms.

The Structural Birnbaum Importance of Consecutive-k Systems

This paper is concerned with three types of structural Birnbaum importance of components in a consecutive-k system. We accomplish the following three tasks:(i) Survey existing results, including pointing out results claimed but proofs are incomplete.(ii) Give some new results and useful lemmas.(iii) Observe what are still provable and what are not with the help of extensive computing.

The towers of Hanoi problem with parallel moves

Abstract This paper proposes a variant of the towers of Hanoi problem allowing parallel moves. An algorithm for this problem is presented and proved to be optimal.

Distance-Preserving and Distance-Increasing Mappings From Ternary Vectors to Permutations

Permutation arrays have found applications in powerline communication. One construction method for permutation arrays is to map good codes to permutations using a distance-preserving mappings (DPM). DPMs are mappings from the set of all q-ary vectors of a fixed length to the set of permutations of some fixed length (the same or longer) such that every two distinct vectors are mapped to permutations with the same or larger Hamming distance than that of the vectors. A DPM is called distance increasing (DIM) if the distances are strictly increased (except when the two vectors are equal). In this correspondence, we propose constructions of DPMs and DIMs from ternary vectors. The constructed DPMs and DIMs improve many lower bounds on the maximal size of permutation arrays.

Topological properties of hierarchical cubic networks

Abstract The hierarchical cubic network (HCN), which takes hypercubes as basic clusters, was first introduced in [6]. Compared with the hypercube of the same size, the HCN requires only about half the number of links and provides a lower diameter. This paper first proposes a shortest-path routing algorithm and an optimal broadcasting algorithm for the HCN. We then show that the HCN is optimal fault tolerant by constructing node-disjoint paths between any two nodes, and demonstrate that the HCN is Hamiltonian. Moreover, it is shown that the average dilation for hypercube emulation on the HCN is bounded by 2. This result guarantees that all the algorithms designed for the hypercube can be executed on the HCN with a small degradation in time performance.

Distributed fault-tolerant routing in Kautz networks

Abstract For a Kautz network with faulty components we propose a distributed fault-tolerant routing scheme, called DFTR, in which each nonfaulty node knows no more than the condition of its links and adjacent nodes. We construct a rooted tree for a given destination in the Kautz network, and use it to develop DFTR such that a faulty component will never be encountered more than once. In DFTR, each node is attempting to route a message via the shortest path. If a node detects a faulty node at the next hop, a best alternative path for routing the message around the faulty component is to be obtained. A best alternative path is first generated by the reduced concatenation of this node and the destination, and then is checked to make sure that it does not contain any of encountered faulty nodes. If it does, a new alternative path is generated as before. We invent an efficient approach in the checking step to reduce computational time. With a slight modification, DFTR may adapt to de Bruijn networks as well.