The purpose of this thesis is to examine the number of edge-disjoint Hamiltonian cycles in de Bruijn graphs using ideas from finite field theory, particularly linear recurring sequences. It is known that the de Bruijn graph B(d,n) admits d-1 disjoint Hamiltonian cycles when d is a power of 2, and...
It is necessary to encode data when transmitting over a noisy channel in order for
errors to be detected and corrected. List decoding algorithms provide all code words
within a specified distance of a received word in order to be sufficiently robust for
cases when two or more code words...
Quotient rings of Gaussian and Eisenstein-Jacobi(EJ) integers can be deployed to construct interconnection networks with good topological properties. In this thesis, we propose deadlock-free deterministic and partially adaptive routing algorithms for hexagonal networks, one special class of EJ networks. Then we discuss higher dimensional Gaussian networks as an alternative to...
If P is an integer polynomial denote the degree of P by ∂(P) and let H(P) be the maximum of the absolute value of the coefficients of P. Define Λ(P)=2[superscript ∂(P)]H(P) and for a fixed prime p let C[subscript p] denote the completion of the algebraic closure of the p-adic...
Interconnection networks play important roles in designing high performance computers. Recently two new classes of interconnection networks based on the concept of Gaussian and Eisenstein-Jacobi integers were introduced. In this research, efficient routing and broadcasting algorithms for these networks are developed. Furthermore, constructing edge disjoint Hamiltonian cycles in Gaussian networks...