Large-scale distributed training increasingly makes collective communication bandwidth-bound. In modern GPU clusters, communication libraries such as NCCL implement collectives including AllReduce over heterogeneous interconnects such as NVLink, InfiniBand, and Ethernet, making efficient use of available network bandwidth a central systems challenge. ForestColl showed that collective communication on such fabrics can be formulated using fractional tree packing; its scalable polynomial-time construction is developed for AllGather, with AllReduce obtained by composing AllGather and ReduceScatter. We present DualColl, which targets bandwidth-bound AllReduce directly. Under the tree-based AllReduce model, DualColl applies a Garg--Könemann-style multiplicative-weights algorithm and, for any $0<ε<1$, computes a feasible schedule whose throughput is at least $(1-ε)^2$ of the optimal AllReduce throughput. Its key component is an exact minimum-cost collective-tree oracle that projects physical-link dual prices onto a logical graph of participating ranks, reducing each iteration to shortest-path computations followed by a minimum spanning tree. We further extend the framework to local equal-next-hop packet-sprayed routing and to networks without explicit per-tree bandwidth control. For the latter, we introduce a tree-coupled max-min bandwidth-sharing model and show that tree duplication approximates an explicit fractional allocation with a provable accuracy-complexity tradeoff. Finally, we extend the fractional-packing framework to additional collective operations and multiple concurrent collective groups.

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