问题
So I've been attempting to analyze a specialized variant of Dijkstras algorithm that I've been working on. I'm after the worst case complexity.
The algorithm uses a Fibonacci Heap which in the case of the normal Dijkstra would run in O(E + V log V).
However this implementation needs to do a lookup in the inner loop where we update neighbours. This lookup will execute for every edge and will be in logarithmic time, where the lookup is in a datastructure that contains all edges. Also the graph has the restriction that no node will have more than 4 neighbours.
O(Vlog V) is the complexity for the outer loop but I'm not sure what the worst case will be for the inner loop. I'm thinking that since that each edge in the graph will be checked O(E) times and each edge will take logarithmic time it should be Elog E which should exceed Vlog V and result in O(Elog E) complexity for the algorithm.
Any insight would be awesome!
回答1:
The amortized complexity of Decrease-Key on Fibonacci Heap is O(1), that is to say you have |E| such operations on the Fibonacci Heap, the total cost will be O(E). Also you have |V| Extract-Min operations, which cost O(lnV) each. So the total cost is O(E+VlnV).
来源：https://stackoverflow.com/questions/26328860/complexity-in-dijkstras-algorithm