Why it matters

Push-relabel is modern max flow standard. Fast in practice.

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The architecture

Preflow + heights.

Push to lower.

Relabel when stuck.

Push-relabel algorithmPreflow + heightsat each vertexPushto lower neighborRelabelwhen stuckGoldberg-Tarjan 1988; fastest in practice for dense graphs
Push-relabel algorithm.
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How it works end to end

Goldberg-Tarjan 1988.

Preflow-based.

Height labels.