Worst Case
Although the total running time of a sequence of operations starting with an empty structure is bounded by the bounds given above, some (very few) operations in the sequence can take very long to complete (in particular delete and delete minimum have linear running time in the worst case). For this reason Fibonacci heaps and other amortized data structures may not be appropriate for real-time systems. It is possible to create a data structure which has the same worst case performance as the Fibonacci heap has amortized performance. However the resulting structure is very complicated, so it is not useful in most practical cases.
Read more about this topic: Fibonacci Heap
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