Fast Response k-Server Problem – 20210626y

I need help with writing code for the below case using C++. this is basically a Dynamic Programming/Graph Traversal problem. the Algorithmic Programs 1. Do not require the user to take any part in the input (“Input the graph, or even input the number of points or input size etc.) FastResponsek-ServerPlacement A series of client machines [1, 2, … n] are located along a linear network. The i- th client generates amount of traffic that is given by w[i] . You want to place k servers along the linear network that minimizes the total amount of traffic carried by the network. Total traffic is given by sum of each client’s individual traffic, multiplied by the distance (the number of hops) from the server. Provide a polynomial-time algorithm to identify the optimal locations for k-servers. the solution should follow: We observe that this algorithm uses O(n^ 2 k) space as there are n ^2 k entries in the dynamic programming table for the variable w . Further, we require O(n) time to compute each entry. Therefore, the algorithm as formulated above takes O(n ^3 k) time. This time complexity can be reduced to O(n ^2 k) time by observing that the “breakpoint” (that is, the point that minimizes weighted cost) for clients i..j+1 can only be after the break point for clients i..j . Therefore, in the loop to compute w(i,j,m) , we do not need to start the break point search from 1 , rather breakpoint for all n values of j can be found in O(n) time. Requirements: as long as the code | .doc file

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