Improved Algorithms for Scheduling Unsplittable Flows on Paths

In this paper, we investigate offline and online algorithms for Round-UFPP, the problem of minimizing the number of rounds required to schedule a set of unsplittable flows of non-uniform sizes on a given path with non-uniform edge capacities. Round-UFPP is NP-hard and constant-factor approximation algorithms are known under the no bottleneck assumption (NBA), which stipulates that maximum size of a flow is at most the minimum edge capacity. We study Round-UFPP without the NBA, and present improved online and offline algorithms. We first study offline Round-UFPP for a restricted class of instances called α-small, where the size of each flow is at most α times the capacity of its bottleneck edge, and present an O(log(1/(1−α)))-approximation algorithm. Our main result is an online O(log log cmax)-competitive algorithm for Round-UFPP for general instances, where cmax is the largest edge capacities, improving upon the previous best bound of O(log cmax) due to [16]. Our result leads to an offline O(min(logn, logm, log log cmax))approximation algorithm and an online O(min(logm, log log cmax))-competitive algorithm for Round-UFPP, where n is the number of flows and m is the number of edges. 1998 ACM Subject Classification F.2.2 Nonnumerical algorithms and Problems