Routing, Broadcasting, Prefix Sums, and Sorting Algorithms on the Arrangement Graph

The (n, k)-arrangement graph A_n,k is a generalization of the well known star graph and the alternating group graph. We first present a constant time routing algorithm that allows two groups of A_n-1,k-1 ´s to exchange their data in a one-to-one fashion. We then use this routing algorithm to develop an optimal broadcasting algorithm, an optimal algorithm for computing the general prefix sums as well as an efficient sorting algorithm on the arrangement graph. Consequently, all of our algorithms are applicable to the star and the alternating group graphs.