THE CONGESTION OF GENERALIZED CUBE COMMUNICATION PATTERN IN LINEAR ARRAY NETWORK

Generalized cubes are a subclass of hypercube-like networks that are employed by a number of parallel algorithms. Linear array is common topology of multicomputer system. So congestion is very useful to improve algorithm performance for implementing generalized cube communication pattern on linear array. This paper addresses the congestion of generalized cube communication patterns embedding into linear array topology. For this purpose, the maximum m-induced subgraph of generalized cube is determined firstly, which is very important for discussing the congestion. Then an embedding scheme is described, and the congestion is shown to attain the minimum, which guarantees the optimality of the proposed scheme.