Data transfers in networks.

The scheduling of the transfer of backlogged data in a network to minimize the finishing time is studied. The most complete treatment (of a version) of the problem is due to Gopal, Bongiovanni, Bonucelli, Tang, and Wong, who attacked the problem using the Birkhoff-von Neumann theorem. However, these authors do not provide a complexity analysis of their algorithm. In this paper we solve the version of these authors as well as a more difficult version of this scheduling problem by formulating them as a continuous form of the Hakimi-Kariv-de Werra generalization of the edge-coloring problem in bipartite graphs. This leads to polynomial time algorithms for these problems. Furthermore, our solution of the previously solved version has the desirable feature of having a tighter bound for the number of 'communication modes' than the solution of the above authors. In the above scheduling problem, there may be a time associated with changing from one set of simultaneous data transfers (i.e., a communication mode) to another. It is shown that if the overall finishing time of our schedule includes these times, then even very simple instances of our problem become NP-hard. However, approximation algorithms are presented which produce solutions whose finishing times are at most twice the optimal. Finally, in the above scheduling problem the interruption (or pre-emption) of the performance of each task is permitted. Essentially, the same problem when pre-emption is not permitted was studied by Coffman, Garey, Johnson, and LaPaugh. The relation between the two problems are explored. [ABSTRACT FROM AUTHOR]