I'm not so good at linear programing so I'm posting this problem here. Hope somebody can point me out to the right direction. It is not homework problem so don't misunderstand.
I have a matrix 5x5 (25 nodes). Distance between each node and its adjacent nodes (or neighbor nodes) is 1 unit. A node can be in 1 of 2 conditions: cache or access. If a node 'i' is a cache node, an access nodes 'j' can be able to access it with a cost of Dij x Aij (Access Cost). Dij is Manhattan distance between node i and j. Aij is access frequency from node i to j.
In order to become a cache node i, it needs to cache from an existing cache node k with a cost of Dik x C where C is a Integer constant. (Cache Cost) . C is called caching frequency.
A is provided as an 25x25 matrix containing all integers that shows access frequency between any pair of node i and j. D is provided as an 25x25 matrix containing all Manhattan distances between any pair of node i and j.
Assume there is 1 cache node in the matrix, find out the set of other cache nodes and access nodes such that the total cost will be minimized. Total Cost = Total Cache Cost + Total Access Cost .