Why it matters

Fibonacci heaps give best Dijkstra bound. Practical win limited by constants.

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The architecture

Lazy meld + decrease-key.

Consolidate on delete-min.

Amortized bounds.

Fibonacci heapLazy meldroot listDecrease-keyamortized O(1)Delete-minconsolidateFredman-Tarjan 1987; best asymptotic Dijkstra; constants often lose to binary heap
Fibonacci heap.
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How it works end to end

Fredman-Tarjan 1987.

Amortized O(1) decrease-key.

Binary heap wins in practice.