Google's framework for the Győri–Lovász theorem also gives a polynomial-time algorithm for Lovász's stronger directed version, a near-linear-time algorithm for DAGs, and polynomial-time algorithms for weighted generalizations known only through nonconstructive existence proofs by Chen, Kleinberg, Lovász, Rajaraman, Sundaram, and Vetta (JACM'07) on confluent flows.
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“The framework also goes further: it gives a polynomial-time algorithm for Lovász’s stronger directed version, a near-linear-time algorithm for DAGs, and polynomial-time algorithms for weighted generalizations previously known only through nonconstructive existence proofs by the seminal work of Chen, Kleinberg, Lovász, Rajaraman, Sundaram, and Vetta (JACM'07) on confluent flows.”
— Mohammad Hajiaghayi|Google team
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