The hypercube topology has multiple paths between nodes and a low overall diameter

of n for a network of 2n nodes. However, these are achieved at the price

of a high node degree. A node must have n ports, which implies that a new node

design is required whenever the size of the network increases. An alternative is

the Cube-Connected Cycles (CCC) which keeps the degree of a node fixed at three

or less. A CCC network that corresponds to the H3 hypercube

Each node of degree three in H3 is replaced by a cycle consisting

of three nodes. In general, each node of degree n in the hypercube Hn is

replaced by a cycle containing n nodes where the degree of every node in the cycle

is 3. The resulting CCC(n,n) network has n2n nodes. In principle, each cycle may

include k nodes with k n with the additional k . n nodes having a degree of 2.

This will yield a CCC(n, k) network with k2n nodes. The extra nodes of degree 2

have a very small impact on the properties that are of interest to us, and we will

therefore restrict ourselves to the case k = n.

The lower degree of nodes in the CCC compared to the hypercube results in a

bigger diameter. Instead of a diameter of size n for the hypercube, the diameter of

the CCC(n,n) is

Dimeter of general CCC network

The routing of messages in the CCC is also more complicated than that in hypercubes.

The fault tolerance of the CCC is, however,

higher because the failure of a single node in the CCC will only have an effect similar

to that of a single faulty link in the hypercube. A closed form expression for

the reliability of the CCC has not yet been derived.

Fault Tolerant Systems Israel Koren C. Mani Krishna

D. S. Meliksetian and C. Y. R. Chen, "Optimal Routing Algorithm and the Diameter of the Cube-

Connected Cycles," IEEE Transactions on Parallel and Distributed Systems, Vol. 4, pp. 1172¨C1178,

October 1993.

The Effect of Using Cube Connected Cyclefor Improving Locality Awareness in Peer-to-Peer Networks

Mohammed Gharib, Zeynab Barzegar, Jafar Habibi Dept. Computer Engineering Sharif University of Technology

Tehran, Iran