Many modern datacenter applications involve large-scale computations composed of multiple data flows that need to be completed over a shared set of distributed resources. Such a computation completes when all of its flows complete. A useful abstraction for modeling such scenarios is a coflow, which is a collection of flows (e.g., tasks, packets, data transmissions) that all share the same performance goal.In this paper, we present the first approximation algorithms for scheduling coflows over general network topologies with the objective of minimizing total weighted completion time. We consider two different models for coflows based on the nature of individual flows: circuits, and packets. We design constant-factor polynomial-time approximation algorithms for scheduling packet-based coflows with or without given flow paths, and circuit-based coflows with given flow paths. Furthermore, we give an O(log n/ log log n)approximation polynomial time algorithm for scheduling circuitbased coflows where flow paths are not given (here n is the number of network edges).We obtain our results by developing a general framework for coflow schedules, based on interval-indexed linear programs, which may extend to other coflow models and objective functions and may also yield improved approximation bounds for specific network scenarios. We also present an experimental evaluation of our approach for circuit-based coflows that show a performance improvement of at least %22 on average over competing heuristics.

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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 c max )-competitive algorithm for Round-UFPP for general instances, where c max is the largest edge capacities, improving upon the previous best bound of O(log c max ) due to [16]. Our result leads to an offline O(min(log n, log m, log log c max ))approximation algorithm and an online O(min(log m, log log c max ))-competitive algorithm for Round-UFPP, where n is the number of flows and m is the number of edges.