Efficient Approximation Algorithms for Scheduling Coflows with Precedence Constraints in Identical Parallel Networks to Minimize Weighted Completion Time (2307.04107v1)

Abstract: This paper focuses on the problem of coflow scheduling with precedence constraints in identical parallel networks, which is a well-known $\mathcal{NP}$-hard problem. Coflow is a relatively new network abstraction used to characterize communication patterns in data centers. Both flow-level scheduling and coflow-level scheduling problems are examined, with the key distinction being the scheduling granularity. The proposed algorithm effectively determines the scheduling order of coflows by employing the primal-dual method. When considering workload sizes and weights that are dependent on the network topology in the input instances, our proposed algorithm for the flow-level scheduling problem achieves an approximation ratio of $O(\chi)$ where $\chi$ is the coflow number of the longest path in the directed acyclic graph (DAG). Additionally, when taking into account workload sizes that are topology-dependent, the algorithm achieves an approximation ratio of $O(R\chi)$, where $R$ represents the ratio of maximum weight to minimum weight. For the coflow-level scheduling problem, the proposed algorithm achieves an approximation ratio of $O(m\chi)$, where $m$ is the number of network cores, when considering workload sizes and weights that are topology-dependent. Moreover, when considering workload sizes that are topology-dependent, the algorithm achieves an approximation ratio of $O(Rm\chi)$. In the coflows of multi-stage job scheduling problem, the proposed algorithm achieves an approximation ratio of $O(\chi)$. Although our theoretical results are based on a limited set of input instances, experimental findings show that the results for general input instances outperform the theoretical results, thereby demonstrating the effectiveness and practicality of the proposed algorithm.