Given an undirected connected graph $G=(V,E)$ with positive weights, where $|V|>2009$, and each vertex is of degree of at most $10$. Give an efficient algorithm to find the $2009$ closest nodes to a given source vertex $s$ (with respect to edge weight).Is it correct to say that Dijkstra's algorithm with Fibonacci heap will run in $\mathcal O(\log V)$? Reasoning:Dijkstra's algorithm with Fibonacci heap runs in $\mathcal O(E+V\log V)$. the amount of vertices pulled out of the heap is $2009$, and the amount of key decreased is at most $2009*10$. Therfore the running time of Dijkstra's algorithm for this case is $\mathcal O(2009*10+2009 \log V)=\mathcal O(\log V)$ 
Shortest path algorithm using Dijkstra with Fibonacci heap
algorithms;shortest path