Louisiana State University LSU Digital Commons LSU Historical Dissertations and Theses Graduate School 1989 Hypercube-Based Topologies With Incremental Link Redundancy. Shahram Latifi Louisiana State University and Agricultural & Mechanical College Follow this and additional works at: https://digitalcommons.lsu.edu/gradschool_disstheses Recommended Citation Latifi, Shahram, "Hypercube-Based Topologies With Incremental Link Redundancy." (1989). LSU Historical Dissertations and Theses. 4788. https://digitalcommons.lsu.edu/gradschool_disstheses/4788 This Dissertation is brought to you for free and open access by the Graduate School at LSU Digital Commons. It has been accepted for inclusion in LSU Historical Dissertations and Theses by an authorized administrator of LSU Digital Commons. For more information, please contact [email protected]. INFORMATION TO USERS The most advanced technology has been used to photo­ graph and reproduce this manuscript from the microfilm master. 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Ann Aibor, MI 48106 HYERCUBE-BASED TOPOLOGIES WITH INCREMENTAL LINK REDUNDANCY A Dissertation Submitted to the Graduate Faculty of the Louisiana State University and Agricultural and Mechanical College in partial fulfillment of the requirements for the degree of Doctor of Philosophy in The Department of Electrical and Computer Engineering by Shah ram Latifi M.S., Teheran university, February 1980 M.S., Louisiana State University, May 1986 August 1989 ACKNOWLEDGEMENTS The author wishes to express his sincere appreciation to Dr. Ahmed El-Amawy, Associate Professor of Electrical Engineering, for his invaluable supervision and gui­ dance of the work represented by this dissertation. Appreciation is also extended to Dr. Owen T. Tan, Dr. Subhash C. Kak, Dr. Surest! Rai of the Electrical and Computer Engineering Department, Dr. J. Bush Jones of the Department of Computer Science, and Dr. Richard Parish of the Department of Agricultural Engineering for serving as members of the examining committee. Above all the author is grateful to his parents, sisters, and brother, whose pati­ ence, understanding, and inspiration have made this study a reality. 11 TABLE OF CONTENTS Acknowledgements ........................................................................................................... ii Table of Contents .............................................................................................................. iii List o f Tables ...................................................................................................................... vii List of Figures .................................................................................................................... viii A bstract ................................................................................................................................ x Chapter 1. Introduction ................................................................................................. 1 1.1 Design Issues ......................................................................................... 5 1.1.1 Network Topologies ............................................................... 5 1.1.2 Control Strategies .................................................................... 6 1.1.3 Network Analysis .................................................................... 7 1.1.4 Reliability .................................................................................. 7 1.1.5 Reconfiguration Techniques .................................................. 8 1.2 Research Objectives ............................................................................. 8 Chapter 2. Review of the Literature ......................................................................... 11 2.1 Hypercube-based N etw orks ................................................................ 19 2.1.1 Nearest Neighbor Mesh ......................................................... 20 2.1.2 Cube-Connected Cycles (CCC) ............................................ 22 2.1.3 Arbitrary Hypercubes ............................. 24 2.1.4 Generalized Hypercubes ......................................................... 24 2.2 Performance Comparison .................................................................... 28 Chapter 3. Notation and Background ....................................................................... 30 111 3.1 Graph Theoretical Model of the n —cube ....................................... 30 3.2 Topological Properties of the n —cube ........................................... 31 3.3 Routing Algorithms in the n-cube ................................................ 33 3.3.1 One to One Routing ................................................................ 33 3.3.2 Broadcasting (One to AH Communication) ........................ 34 3.3.2.1 Spanning Binomial T ree .......................................... 35 3.3.2.2 Multiple Spanning Binomial T ree ......................... 37 3.3.3 Communication Complexity of SBT- and MSBT-based Broadcasting ................................................... 38 3.3.3.1 Spanning Binomial Tree ............................................. 38 3.3.3.2 Multiple Spanning Binomial Tree ............................ 38 3.4 Network Parameters for the n -cube .............................................. 40 3.4.1 Average Distance (d ) .............................................................. 40 3.4.2 Diameter (d) ............................................................................. 40 3.4.3 Cost (v ) ...................................................................................... 40 3.4.4 Message Traffic Density (p) .................................................. 41 3.4.5 Average Message Delay (7*) ................................................ 41 3.5 Fault Tolerance Capabilities of the n - c u b e .................................. 43 3.5.1 Connectivity .......................... ................................................... 43 3.5.2 Two-Terminal Reliability ....................................................... 43 3.5.3 Container ................................................................................... 43 3.5.4 / -Fault Diameter ..................................................................... 44 Chapter 4. Bridged Hypercubes ................................................................................. 45 4.1 Reducing the Network Diameter ...................................................... 46 iv 4.2 The Bridged Hypercube (BHC) ......................... .............................. 47 4.2.1 One to One Routing in BHC ................................................. 48 4.2.2 Broadcasting in BHC ............................................................... 58 4.3 Narrow Bridged Hypercube ............................................................. 62 4.3.1 One to One Routing in NBHC .............................................. 63 4.3.2 Broadcasting in NBHC .......,.................................................. 63 4.4 Performance Analysis of BHC and NBHC .................................... 65 Chapter 5. Folded Hypercubes .................................................................................... 69 5.1 The Structure of the Folded Hypercube (FHC) ............................ 69 5.2 Graph Theoretical Model of the FH C ............................................. 69 5.3 Topological Properties of the FHC ................................................ 70 5.4 Routing Algorithms in the FHC ...................................................... 77 5.4.1 One to One Routing ................................................................ 77 5.4.2 Broadcasting .............................................................................. 78 5.4.2.1 Spanning Binary Tree for the FHC (SBTF) .......................................................................