Associative parallel algorithms for computing functions defined on paths in trees

Abstract

By means of an abstract model of the SIMD type with vertical data processing (the STAR-machine), we present a simple associative parallel algorithm for finding tree paths in undirected graphs. We study applications of this algorithm to update minimum spanning trees in undirected graphs, to determine maximum flow values in a multiterminal network, and to find a fundamental set of circuits with respect to a given spanning tree. These algorithms are given as the corresponding STAR procedures whose correctness is proved and time complexity is evaluated.