Why it matters

Borůvka parallelizes well. Foundation for parallel MST.

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The architecture

Round: each component picks cheapest outgoing edge.

Merge components.

Repeat log V rounds.

Borůvka roundsEach componentpicks min outgoingMergechosen edgesRepeatlog V roundsLog V rounds because component count halves per round
Borůvka.
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How it works end to end

Log V rounds (component count halves).

Each round: O(E).

Parallel: rounds sequential; within round parallel.