Concentration, load balancing, partial permutation routing, and superconcentration on cube-connected cycles parallel computers

The cube-connected cycles (CCC) was proposed by Preparata and Vuillemin as an efficient general-purpose parallel system for its fixed-degree, and compact and regular layout. In this paper, a few of the basic algorithms on CCC(n,2n) interconnection networks are addressed and then applied to concentration, superconcentration, partial permutation routing, and load-balancing problems. The results show that both concentration and superconcentration problems can be solved in O(n) time and the on-line partial permutation routing problem in O(n2) time with O(1) buffers for each node, where n is the dimension of CCC(n,2n) interconnection networks. The load-balancing problem based on superconcentration can be solved in O(Mn) time, where M is the maximum number of tasks in each node.