Novel data communication algorithms on hypercubes and related interconnection networks and their applications in computational geometry

In an interconnection network where each processor stores several data items, many algorithms are based on a pipelining approach. The latter typically implies that an embedding of another network into the network at hand is known. The resulting algorithms are usually complicated to implement and involve a considerable amount of computational overhead. In addition, by using special embeddings and pipelining, some of the properties of the underlying interconnection network are not used advantageously. In this paper, we first develop several data communication algorithms for the hypercube without resorting to pipelining. These algorithms exploit the standard ASCEND/DESCEND schemes which are common for hypercube-like networks. The implementations are simple and their performances match those of previous algorithms that invoke embeddings and pipelining. More significantly, these algorithms can be easily applied to similar interconnection networks without having to find some embeddings first in order to use the technique of pipelining. In addition, me apply the data communication algorithms developed here to obtain several parallel algorithms on hypercubes and other networks for some problems in computational geometry: locating multiple points in a simple polygon and in a planar subdivision. These algorithms' performances either match those of previous ones or surpass them in some cases.