# perl-Algorithm-Munkres

Munkres.pm

Assignment Problem: Given N jobs, N workers and the time taken by each worker to complete a job then how should the assignment of a Worker to a Job be done, so as to minimize the time taken. Thus if we have 3 jobs p,q,r and 3 workers x,y,z such that: x y z p 2 4 7 q 3 9 5 r 8 2 9 where the cell values of the above matrix give the time required for the worker(given by column name) to complete the job(given by the row name) then possible solutions are: Total 1. 2, 9, 9 20 2. 2, 2, 5 9 3. 3, 4, 9 16 4. 3, 2, 7 12 5. 8, 9, 7 24 6. 8, 4, 5 17 Thus (2) is the optimal solution for the above problem. This kind of brute-force approach of solving Assignment problem quickly becomes slow and bulky as N grows, because the number of possible solution are N! and thus the task is to evaluate each and then find the optimal solution.(If N=10, number of possible solutions: 3628800 !) Munkres' gives us a solution to this problem, which is implemented in this module. This module also solves Assignment problem for rectangular matrices (M x N) by converting them to square matrices by padding zeros. ex: If input matrix is: [2, 4, 7, 9], [3, 9, 5, 1], [8, 2, 9, 7] i.e 3 x 4 then we will convert it to 4 x 4 and the modified input matrix will be: [2, 4, 7, 9], [3, 9, 5, 1], [8, 2, 9, 7], [0, 0, 0, 0]

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