You may find the ideas in 
http://www.eecs.harvard.edu/~parkes/cs286r/spring02/papers/vickrey.pdf
interesting.

On May 17, 2:44 pm, vivek dhiman <[email protected]> wrote:
> Please help me solve this problem for cases with high number of nodes. I am
> getting time limit exceeded.
>
> Ms.Kox enjoys a nice job of her interest, but she does not like to waste
> much time on going-to/coming-from office. She is now aware of the route to
> her office that has the smallest distance, after all she has been working
> there for past five years.
>
> The recent maintenance of roads that has started is an issue now. Every day
> a road gets blocked because of the maintenance and no one can use it that
> day( however all other roads can be used). You are her new intern and this
> task is for you. You need to determine for each day the minimum distance
> that she has to travel to reach her office.
>
> *Input Format:*
>
> There are N cities numbered 0 to N-1 and M bidirectional roads.
> First line of the input contains two integers N and M.
> Then follows M lines each containing three space-separated integers u , v
> and w, which means that there is a bi-directional road connecting city u
> and city v , and w is the length of this road.There is at most one road
> between any two cities and no road connects a city to itself.
> Next line contains two integers S and D, S is the city in which Mr. Kox
> lives and D is the city in which her office is located.
> Next line contains an integer Q, the number of queries.
> Then follows Q lines each containing two integers u and v , which tells
> that the road between city u and city v is blocked on that day.
>
> *Output Format:*
>
> Q lines , each line containing minimum distance Ms.Kox has to travel on
> that day.If there is no path print *"Infinity"* (quotes for clarity).
>
> *Constraints:*
> 0 < N < 200,000
> 0 < M < 200,000
> 0 < Q < 200,000
> 0 <= S , D < N
>
> *Sample input:*
>
> 6 9
> 0 1 1
> 1 2 1
> 2 3 1
> 3 4 1
> 4 5 1
> 2 4 5
> 3 5 8
> 1 3 3
> 0 2 4
> 0 5
> 9
> 0 1
> 1 2
> 2 3
> 3 4
> 4 5
> 2 4
> 3 5
> 1 3
> 0 2
>
> *
> *
>
> *Sample output :*
>
> 7
> 6
> 6
> 8
> 11
> 5
> 5
> 5
> 5
>
> *
> *

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