Opened 8 years ago

Closed 8 years ago

#4852 closed Bugs (fixed)

Wrong complexity of Dijkstra algorithm

Reported by: erelsgl@… Owned by: Andrew Sutton
Milestone: To Be Determined Component: graph
Version: Boost 1.44.0 Severity: Problem
Keywords: Cc:


In this page: and this page:

you say that "The time complexity is O(V log V)".

However, any shortest-paths algorithm must, at the worst case, visit each edge at least once, so the worst-case time complexity must contain a term that depends on E.

According to Wikipedia: , the running time is O(E + V log V) if you use a Fibonacci heap.

Also, note that in this page:

you say that for a DAG, "The time complexity is O(V + E)", and it is generally more efficient than Dijkstra's algorithm. However, in the worst case, E might be O(V2), which is worst than V log V!

Change History (2)

comment:1 Changed 8 years ago by Daniel James

Component: Documentationgraph
Owner: changed from Matias Capeletto to Andrew Sutton

comment:2 Changed 8 years ago by Jeremiah Willcock

Resolution: fixed
Status: newclosed

(In [66960]) Fixed complexity of Dijkstra's algorithm; fixes #4852

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