Tseng-Kuei Li

Fault hamiltonicity and fault hamiltonian connectivity of the arrangement graphs

The arrangement graph A/sub n,k/ is a generalization of the star graph. There are some results concerning fault Hamiltonicity and fault Hamiltonian connectivity of the arrangement graph. However, these results are restricted in some particular cases and, thus, are less completed. We improve these results and obtain a stronger and simpler statement. Let n-k/spl ges/2 and F/spl sube/V(A/sub n,k/)/spl cup/E(A/sub n,k/). We prove that A/sub n,k/-F is Hamiltonian if |F|/spl les/k(n-k)-2 and A/sub n,k/-F is Hamiltonian connected if |F|/spl les/k(n-k)-3. These results are optimal.

Hyper hamiltonian laceability on edge fault star graph

The star graph possess many nice topological properties. Edge fault tolerance is an important issue for a network since the edges in the network may fail sometimes. In this paper, we show that the n-dimensional star graph is (n - 3)-edge fault tolerant hamiltonian laceable, (n - 3)-edge fault tolerant strongly hamiltonian laceable, and (n - 4)- edge fault tolerant hyper hamiltonian laceable. All these results are optimal in a sense described in this paper.

Fault-tolerant cycle-emebedding of crossed cubes

The crossed cube CQn introduced by Efe has many properties similar to those of the popular hypercube. However, the diameter of CQn is about one half of that of the hypercube. Failures of links and nodes in an interconnection network are inevitable. Hence, in this paper, we consider the hybrid fault-tolerant capability of the crossed cube. Letting fe and fv be the numbers of faulty edges and vertices in CQn, we show that a cycle of length l, for any 4 ≤ l ≤ |V(CQn)| - fv, can be embedded into a wounded crossed cube as long as the total number of faults (fv + fv) is no more than n - 2, and we say that CQn is (n - 2)-fault-tolerant pancyclic. This result is optimal in the sense that if there are n - 1 faults, there is no guarantee of having a cycle of a certain length in it.

A fast fault-identification algorithm for bijective connection graphs using the PMC model

Diagnosis of reliability is an important topic for interconnection networks. Under the classical PMC model, Dahura and Masson [5] proposed a polynomial time algorithm with time complexity O(N^2^.^5) to identify all faulty nodes in an N-node network. This paper addresses the fault diagnosis of so called bijective connection (BC) graphs including hypercubes, twisted cubes, locally twisted cubes, crossed cubes, and Mobius cubes. Utilizing a helpful structure proposed by Hsu and Tan [20] that was called the extending star by Lin et al. [24], and noting the existence of a structured Hamiltonian path within any BC graph, we present a fast diagnostic algorithm to identify all faulty nodes in O(N) time, where N=2^n, n>=4, stands for the total number of nodes in the n-dimensional BC graph. As a result, this algorithm is significantly superior to Dahura-Massons algorithm when applied to BC graphs.

The shuffle-cubes and their generalization

In this paper, we first present a new variation of hypercubes, denoted by SQn. SQn is obtained from Qn by changing some links. SQn is also an n-regular n-connected graph but of diameter about n=4. Then, we present a generalization of SQn .F or any positive integer g, we can construct an n-dimensional generalized shuffle-cube with 2 n vertices which is n-regular and n-connected. However its diameter can be about n=g if we consider g as a constant.

A dynamic programming algorithm for simulation of a multi-dimensional torus in a crossed cube

The torus is a popular interconnection topology and several commercial multicomputers use a torus as the basis of their communication network. Moreover, there are many parallel algorithms with torus-structured and mesh-structured task graphs have been developed. If one network can embed a mesh or torus network, the algorithms with mesh-structured or torus-structured can also be used in this network. Thus, the problem of embedding meshes or tori into networks is meaningful for parallel computing. In this paper, we prove that for n?6 and 1≤m≤?n/2?-1, a family of 2m disjoint k-dimensional tori of size 2 s 1 × 2 s 2 × ? × 2 s k each can be embedded in an n-dimensional crossed cube with unit dilation, where each si?2, ? i = 1 k s i = n - m , and max1≤i≤k{si}?3 if n is odd and m = n - 3 2 ; otherwise, max1≤i≤k{si}?n-2m-1. A new concept, cycle skeleton, is proposed to construct a dynamic programming algorithm for embedding a desired torus into the crossed cube. Furthermore, the time complexity of the algorithm is linear with respect to the size of desired torus. As a consequence, a family of disjoint tori can be simulated on the same crossed cube efficiently and in parallel.

Hamiltonian laceability on edge fault star graph

The star graph is an attractive alternative to the hypercube graph. It possess many nice topological properties. Edge fault tolerance is an important issue for a network since the edges in the network may fail sometimes. In this paper, we show that the n-dimensional star graph is (n-3)-edge fault tolerant hamiltonian laceable, (n-3)-edge fault tolerant strongly Hamiltonian laceable, and (n-4)-edge fault tolerant hyper Hamiltonian laceable. All these results are optimal in a sense described in this paper.

OPTIMUM CONGESTED ROUTING STRATEGY ON TWISTED CUBES

Given a shortest path routing algorithm of an interconnection network, the edge congestion is one of the important factors to evaluate the performance of this algorithm. In this paper, we consider the twisted cube, a variation of the hypercube with some better properties, and review the existing shortest path routing algorithm8. We find that its edge congestion under the routing algorithm is high. Then, we propose a new shortest path routing algorithm and show that our algorithm has optimum time complexity O(n) and optimum edge congestion 2n. Moreover, we calculate the bisection width of the twisted cube of dimension n.

Embedding a k-D Torus into a Locally Twisted Cube

The locally twisted cube is one of the most notable variations of hypercube, but some properties of the locally twisted cube are superior to those of the hypercube. For example, the diameter of former is almost the half of that of the later. This paper addresses how to embed a maximal size of multi-dimensional torus into a locally twisted cube. The major contribution of this paper is that for

Efficient Algorithms for Embedding Cycles in Augmented Cubes

n\ge 4