Question

NASA wants to link n stations spread over the country using communication channels. Each pair of stations has a different bandwidth available, which is known a priori. NASA wants to select n − 1 channels (the minimum possible) in such a way that all the stations are linked by the channels and the total bandwidth (defined as the sum of the individual bandwidths of the channels) is maximum.

Give an efficient algorithm for this problem and determine its worst-case time complexity. Consider the weighted graph G = (V, E), where V is the set of stations and E is the set of channels between the stations. Define the weight w(e) of an edge e ∈ E as the bandwidth of the corresponding channel.

I am not looking for pseudo code. Will not rate positively if given pseudo code.

Answer 1

In the given question it was described that NASA wants to link n number of stations and each pair of stations has a different bandwidth.

Here we have to write a efficient algorithm for the problem and have to determine the worst-case time.

So below we have written an algorithm for the given question:

1. Begin

2. create a graph G of n stations.

3. Find max bandwidth

4. If cycle is not created add to MST.

5. Repeat 4 & 5

6. END

Hence we have written an efficient algorithm to determine the bandwidth and weight of an edge using above algorithm.