Coflow provides a key application-layer abstraction for capturing communication patterns, enabling the efficient coordination of parallel data flows to reduce job completion times in distributed systems. Modern data center networks (DCNs) are employing multiple independent optical circuit switching (OCS) cores operating concurrently to meet the massive bandwidth demands of application jobs. However, existing coflow scheduling research primarily focuses on the single-core setting, with multi-core fabrics only for EPS (electrical packet switching) networks. To address this gap, this paper studies the coflow scheduling problem in multi-core OCS networks under the \textit{not-all-stop} reconfiguration model in which one circuit's reconfiguration does not interrupt other circuits. The challenges stem from two aspects: (i) cross-core coupling induced by traffic assignment across heterogeneous cores; and (ii) per-core OCS scheduling constraints, namely \textit{port exclusivity} and \textit{reconfiguration delay}. We propose an approximation algorithm that jointly integrates cross-core flow assignment and per-core circuit scheduling to minimize the total weighted coflow completion time (CCT) and establish a provable worst-case performance guarantee. Trace-driven simulations using real Facebook workloads demonstrate that our algorithm effectively reduces weighted CCT and tail CCT.

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