Study on optimal topology for computer local double loop networks

A dist ributed optimal local double loop (DOLDL) network is presented. Emphasis is laid on the topology and distributed routing algorithms for the DOLDL. On the basis of building an abstract model, a set of definitions and theorems are described and proved. An algorithm which can optimize the double loop networks is presented. The optimal values of the topologic parameters for the DOLDL have been obtained by the algorithm, and these numerical results are analyzed. The study shows that the bounds of the optimal diameter d and average hop distance a for this class of networks are
$[\sqrt{3N}-2]\leq d \leq [\sqrt{3N}]$
and
$(5N/9(N-1))\cdot (\sqrt{3N}-1.8) < a < (5N/9(N-1))\cdot (\sqrt{3N}-0.9)
, respectively (N is the number of nodes in the network). A class of the distributed routing algorithms for the DOLDL and the implementation procedure of an adaptive fault — tolerant algorithm are proposed and analyzed. The correctness of the algorithm has also been verified by simulating.