A framework of cycle-based clustering on the crossed cube architecture

For large-scale networking environments, grouping network nodes into clusters is a key technique to achieve the scalability objective. This paper addresses cycle-based node clustering in the crossed cube architecture. Let r be a positive integer. For any r distinct vertices v(1), ..., v(r) of a network G = (V, E), G is said to be spanning (v(1), ..., v(r))-cyclable if there exists a set of r vertex-disjoint cycles C-1, ..., C-r in G such that min{l(C-1), ..., l(C-r)} >= 4, Sigma(r)(i=1) l(C-i) = vertical bar V vertical bar, and v(i) is an element of V(C-i) for 1 <= i <= r, where l(C-i) denotes the length of cycle C-i, vertical bar V vertical bar is the total number of vertices in G, and V(C-i) denotes the set of vertices traversed by C-i. Then, C-1, ..., C-r form a collection of r clusters indexed by cluster heads v(1), ..., v(r).