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  Course No: S07010461     Credit: 4        Periods: 80

    Combinatorial Network Theory  

Required textbook: Junming Xu, Topological Structure and Analysis of Interconnection Networks. Kluwer Academic Publishers, October, 2001

Background of Course:  The advent of very large scale integrated (VLSI) circuit technology has enabled the construction of very complex and large interconnection networks. By most accounts, the next generation of supercomputers will achieve its gains by increasing the number of processing elements, rather than by using faster processors. The most difficult technical problem in constructing a supercomputer will be the design of the interconnection network through which the processors communicate. Selecting an appropriate and adequate topological structure of interconnection networks will become a critical issue. Graph theory is a fundamental and powerful mathematical tool for designing and analyzing interconnection networks, since an interconnection network is able to be represented as a graph whose vertices represent components of the network and whose edges represent physical communication links. Such a graph is called the topological structure of the interconnection network. Thus, we may enjoy the methods in graph theory to study the structure of networks, on which many research efforts have been made over the past decade.

Course Description:  This course provides the most basic problems, concepts, and well-established results from the topological structure interconnection networks in the graph-theoretic language. It covers the basic principles and methods of network design, several well-known networks such as hypercube, de Bruijn digraph, Kautz digraph, double loop, and others, and the newest parameters to measure performance of fault-tolerant networks such as forwarding index of a routing, Menger number, Rabin number, fault-tolerant diameter, wide-diameter, restricted connectivity and diameter, and (l, w)-dominating number. 

    Audience:  Postgraduate Students (Ph. D and M. S)

    Preparatory Courses:  Abstract Algebra, Combinatorics, Graph Theory

    Test Form:  Written Examination