Mapping dynamic data and algorithm structures into product networks

Abstract

This paper presents optimal dynamic embeddings of dynamically growing or shrinking trees and three types of dynamically evolving grids into the de Bruijn graphs, and product networks such as (generalized) hypercube, hyper-de Bruijn, hyper Petersen, folded Petersen and product-shuffle networks. Our results are important in mapping data and algorithm structures into multiprocessor interconnection networks. Tree embeddings can be used to maintain dynamic data structures such as quad-trees in image processing or data dictionaries, or to efficiently parallelize tree-based computations in divide-and-conquer or branch-and-bound algorithms. Dynamic embeddings of grids are used to parallelize solution methods for partial differential equations, for adaptive mesh refinement or hierarchical domain decomposition in approximation and interpolation of surfaces, image processing, or dynamic programming algorithms.