CONSTRUCTION SCHEMES OF THE OPTIMAL FAULT-TOLERANT NETWORKS FOR RINGS AND LINEAR ARRAYS
朱孝深、洪春男
E-mail: [email protected]
ABSTRACT
AN INTERCONNECTION NETWORK CONNECTS THE PROCESSORS OF THE PARALLEL COMPUTER. THE RING AN -D LINEAR ARRAY NETWORKS ARE THE MOST FUNDAMENTAL TOPOLOGIES FOR
INTERCONNECTION NETWORKS. THEY CAN BE USED TO SORTING AND SEARCHING DATA IN
DISTRIBUTED SYSTEMS.A RING NETWORK IS AL -SO USED AS A CONNECTION STRUCTURE FOR LOCAL AREA NETWORKS,FOR EXAMPLE TOKEN RINGS.FAULT TOLERANCE IS ALSO AN IMPORTANT ISSUE
ESPECIALLY WHEN THE SIZE OF AN INTERCONNECTION NETWOR -K IS LARGE. IN THIS THESIS,WE STUDY THE FAULT TOLERANCE PROPERTIES AND CONSTRUCTION SCHEM -ES FOR RING AND LINEAR ARRAY NETWORKS WITH BOTH NODES AND LINKS FAILURES. IN THIS THESIS,WE INTRODUCE THE CONCEPTS OF (NODE, EDGE) HAMILTONIAN-CONNECTIVITY AND ST RONGLY K-HAMILTONIAN GRAPH.
FURTHERMORE,WE PRESENT CONSTRUCTION SCHEMES FOR FAULT-TOLERANT HAMILTONIAN AND HAMILTONIAN-CONNECTED NETWORKS. WE WILL STUDY A NEW CONCEPT, CALLED STRONGLY
K-HAMILTONIAN GRAPHS, FOR THE FAULT TOLERANCE OF HAMILTONIAN GRAPHS. WE ALSO PRESENT TWO CONSTRUCTION SCHEMES FOR STRONGLY K-HAMILTONIAN GRAPHS INCLUDING (K + 2)-JOIN AND CARTESIAN PRODUCT WITH K2.APPLYING THESE SCHEMES,WE CAN CONSTRUCT MANY NEW STRONGLY K-HAMILTONIAN GRAPHS.
Keywords : K-HAMILTONIAN, (K+2)-JOIN, INTERCONNECTION NETWORK, (NODE, EDGE)
HAMILTONIAN-CONNECTIVITY, STRONGLY K-HAMILTONIAN GRAPHS, CARTESIAN PRODUCT, FAULT TOLERANCE.
Table of Contents
Contents 封面內頁 簽名頁 授權書 iii 中文摘要 v ABSTRACT vi 誌謝 vii Contents viii List of Figures ix Chapter 1 Introduction and definitions 1 Chapter 2 Construction for fault-tolerant Hamiltonian and Hamiltonian-connected graphs 4 2.1
Hamiltonian-connectivity, node-Hamiltonian-connectivity and edge-Hamiltonian-connectivity 4 2.2 Construction schemes for fault tolerance of Hamiltonian and Hamiltonian-connected graphs 6 Chapter 3 Construction for strongly k-Hamiltonian graphs 30 3.1 Strongly k-Hamiltonian graphs and (k + 2)-join operation 30 3.2 Strongly k-Hamiltonian graphs and Cartesian product operation 36 Chapter 4 Conclusions and future works 43 Bibliography 44 Vita 48
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