Why it matters

Edge-disjoint paths measure connectivity. Understanding shapes reliability.

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The architecture

Unit-capacity max flow.

Menger: max EDP = min cut.

Solve via Dinic.

Edge-disjoint pathsUnit capacities1 per edgeMax flowDinic O(E sqrt V)= max EDPby MengerVertex-disjoint variant: split vertices with unit capacity edge
EDP.
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How it works end to end

Set edge caps to 1.

Run max flow.

Value = max EDP.

Decompose flow into paths.