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...
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...
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...
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...
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...