Dajin Wang

Diagnosability of hypercubes and enhanced hypercubes under the comparison diagnosis model

A. Sengupta and A. Dahbura (1992) discussed how to characterize a diagnosable system under the comparison diagnosis model proposed by J. Maeng and M. Malek (1981) and a polynomial algorithm was given to identify the faulty processors provided that the systems diagnosability is known. However, for a general system, the determination of its diagnosability is not algorithmically easy. This paper proves that, for the important hypercube structured multiprocessor systems (n-cubes), the diagnosability under the comparison model is n when n/spl ges/5. The paper also studies the diagnosability of enhanced hypercube, which is obtained by adding 2/sup n-1/ more links to a regular hypercube of 2/sup n/ processors. It is shown that the augmented communication ability among processors also increases the systems diagnosability under the comparison model. We prove that the diagnosability is n+1 for an enhanced hypercube when n/spl ges/6.

Embedding Hamiltonian Cycles into Folded Hypercubes with Faulty Links

It has been known that an n-dimensional hypercube (n-cube for short) can always embed a Hamiltonian cycle when the n-cube has no more than n?2 faulty links. In this paper, we study the link-fault tolerant embedding of a Hamiltonian cycle into the folded hypercube, which is a variant of the hypercube, obtained by adding a link to every pair of nodes with complementary addresses. We will show that a folded n-cube can tolerate up to n?1 faulty links when embedding a Hamiltonian cycle. We present an algorithm, FT_HAMIL, that finds a Hamiltonian cycle while avoiding any set of faulty links F provided that |F|?n?1. An operation, called bit-flip, on links of hyper-cube is introduced. Simple yet elegant, bit-flip will be employed by FT_HAMIL as a basic operation to generate a new Hamiltonian cycle from an old one (that contains faulty links). It is worth pointing out that the algorithm is optimal in the sense that for a folded n-cube, n?1 is the maximum number for |F| that can be tolerated, F being an arbitrary set of faulty links.

On Embedding Hamiltonian Cycles in Crossed Cubes

We study the embedding of Hamiltonian cycle in the Crossed Cube, which is a prominent variant of the classical hypercube, obtained by crossing some straight links of a hypercube, and has been attracting much research interest in literatures since its proposal. We will show that due to the loss of link-topology regularity, generating Hamiltonian cycles in a crossed cube is a more complicated procedure than in its original counterpart. The paper studies how the crossed links affect an otherwise succinct process to generate a host of well-structured Hamiltonian cycles traversing all nodes. The condition for generating these Hamiltonian cycles in a crossed cube is proposed. An algorithm is presented that works out a Hamiltonian cycle for a given link permutation. The useful properties revealed and the algorithm proposed in this paper can find their way when system designers evaluate a candidate networks competence and suitability, balancing regularity and other performance criteria, in choosing an interconnection network.

A New Fault-Information Model for Adaptive & Minimal Routing in 3-D Meshes

In this paper, we rewrite the minimal-connected-component (MCC) model in 2-D meshes in a fully-distributed manner without using global information so that not only can the existence of a Manhattan-distance-path be ensured at the source, but also such a path can be formed by routing-decisions made at intermediate nodes along the path. We propose the MCC model in 3-D meshes, and extend the corresponding routing in 2-D meshes to 3-D meshes. We consider the positions of source & destination when the new faulty components are constructed. Specifically, all faulty nodes will be contained in some disjoint fault-components, and a healthy node will be included in a faulty component only if using it in the routing will definitely cause a non-minimal routing-path. A distributed process is provided to collect & distribute MCC information to a limited number of nodes along so-called boundaries. Moreover, a sufficient & necessary condition is provided for the existence of a Manhattan-distance-path in the presence of our faulty components. As a result, only the routing having a Manhattan-distance-path will be activated at the source, and its success can be guaranteed by using the information of boundary in routing-decisions at the intermediate nodes. The results of our Monte-Carlo-estimate show substantial improvement of the new fault-information model in the percentage of successful Manhattan-routing conducted in 3-D meshes.

The Extra Connectivity and Conditional Diagnosability of Alternating Group Networks

Extra connectivity, diagnosability, and conditional diagnosability are all important measures for a multiprocessor systems ability to diagnose and tolerate faults. In this paper, we analyze the fault tolerance ability for the alternating group graph, a well-known interconnection network proposed for multiprocessor systems, establish the h-extra connectivity, where 1 ≤ h ≤ 3, and prove that the conditional diagnosability of an n-dimensional alternating group graph, denoted by AGn, is 8n - 27 (n ≥ 4) under the PMC model. This is about four times of the AGns traditional diagnosability. As a byproduct, the strong diagnosability of AGn is also obtained.

A new fault information model for fault-tolerant adaptive and minimal routing in 3-D meshes

In this paper we rewrite Wangs Minimal-Connected-Component (MCC) model in 2D meshes without using global information so that not only the existence of a minimal path can be ensured at the source, but also such a path can be formed by routing decisions at intermediate nodes along the path. We extend this MCC model and the corresponding routing in 2D meshes to 3D meshes. It is based on our early work on fault tolerant adaptive and minimal routing and the boundary information model in 3D meshes. We study fault tolerant adaptive and minimal routing from the source and the destination and consider the positions of the source and destination when the new faulty components are constructed. Specifically, all faulty nodes will be contained in some disjoint faulty components and a healthy node will be included in a faulty component only if using it in the routing will definitely cause a non-minimal routing path. A sufficient and necessary condition is proposed for the existence of the minimal routing path in the presence of our faulty components. Based on such a condition, the corresponding routing will guarantee a minimal path whenever it exists.

Clustering mesh-like wireless sensor networks with an energy-efficient scheme

We study the problem of appropriately clustering mesh-like Wireless Sensor Networks (WSNs). That is, to impose a hierarchical structure on a WSN of mesh-topology, how many clusterhead nodes we should assign, and how to geographically allocate these clusterheads. Since a clustering method that optimises all factors is impossible to achieve, we will focus on the crucial issue of energy efficiency of the WSN. Because it is mostly true that the nodes of WSN are powered by batteries, power saving is an especially important consideration in WSN architecture design. Based on analytical results, a clustering scheme is proposed for WSN towards the end of saving energy of both sensor nodes and clusterhead nodes.

The

The t/k-diagnosis is a diagnostic strategy at system level that can significantly enhance the systems self-diagnosing capability. It can detect up to t faulty processors (or nodes, units) which might include at most k misdiagnosed processors, where k is typically a small number. Somani and Peleg ([26], 1996) claimed that an n-dimensional Star Graph (denoted Sn), a well-studied interconnection model for multiprocessor systems, is ((k + 1)n - 3k - 2)/k-diagnosable. Recently, Chen and Liu ([5], 2012) found counterexamples for the diagnosability obtained in [26], without further pursuing the cause of the flawed result. In this paper, we provide a new, complete proof that an n-dimensional Star Graph is actually ((k + 1)n - 3k - 1)/k-diagnosable, where 1 ≤ k ≤ 3, and investigate the reason that caused the flawed result in [26]. Based on our newly obtained fault-tolerance properties, we will also outline an O(N log N) diagnostic algorithm ( N = n! is the number of nodes in Sn) to locate all (up to (k + 1)n - 3k - 1) faulty processors, among which at most k (1 ≤ k ≤ 3) fault-free processors might be wrongly diagnosed as faulty.

t/k

We study the problem of assigning clusterheads in a hierarchical Wireless Sensor Network (WSN). That is, for a given hierarchical WSN, how many clusterhead nodes we should assign, and how to geographically allocate these clusterheads. Since an assignment scheme optimizing all factors is impossible, we will focus on the crucial issue of energy efficiency of the WSN. Because it is mostly true that the nodes of WSN are powered by batteries, power saving is an especially important consideration in WSN architecture design. We will propose a hierarchical WSN architecture toward the end of saving energy of both sensor nodes and clusterheads. Using analytical result, experiments are conducted in which realistic scenarios are simulated.

-Diagnosability of Star Graph Networks

The crossed cube is a prominent variant of the well known, highly regular-structured hypercube. In [24], it is shown that due to the loss of regularity in link topology, generating Hamiltonian cycles, even in a healthy crossed cube, is a more complicated procedure than in the hypercube, and fewer Hamiltonian cycles can be generated in the crossed cube. Because of the importance of fault-tolerance in interconnection networks, in this paper, we treat the problem of embedding Hamiltonian cycles into a crossed cube with failed links. We establish a relationship between the faulty link distribution and the crossed cubes tolerability. A succinct algorithm is proposed to find a Hamiltonian cycle in a CQn tolerating up to n-2 failed links.