Any directed graph admits a sparse DAG projection of size m^{1+o(1)} that (1+1/polylog n)-approximates all-pairs distances or n^{o(1)}-approximates subset maximum flows.
Negative-weight single-source shortest paths in near-linear time: Now faster! In FOCS , pages 515--538
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DAG Projections: Reducing Distance and Flow Problems to DAGs
Any directed graph admits a sparse DAG projection of size m^{1+o(1)} that (1+1/polylog n)-approximates all-pairs distances or n^{o(1)}-approximates subset maximum flows.