dlib/python_examples/max_cost_assignment.py

#!/usr/bin/python
# The contents of this file are in the public domain. See LICENSE_FOR_EXAMPLE_PROGRAMS.txt
#
# 
# This simple example shows how to call dlib's optimal linear assignment problem solver.
# It is an implementation of the famous Hungarian algorithm and is quite fast, operating in
# O(N^3) time.
#
# COMPILING THE DLIB PYTHON INTERFACE
#   Dlib comes with a compiled python interface for python 2.7 on MS Windows.  If
#   you are using another python version or operating system then you need to
#   compile the dlib python interface before you can use this file.  To do this,
#   run compile_dlib_python_module.bat.  This should work on any operating system
#   so long as you have CMake and boost-python installed.  On Ubuntu, this can be
#   done easily by running the command:  sudo apt-get install libboost-python-dev cmake


import dlib

# Let's imagine you need to assign N people to N jobs.  Additionally, each person will make
# your company a certain amount of money at each job, but each person has different skills
# so they are better at some jobs and worse at others.  You would like to find the best way
# to assign people to these jobs.  In particular, you would like to maximize the amount of
# money the group makes as a whole.  This is an example of an assignment problem and is
# what is solved by the dlib.max_cost_assignment() routine.

# So in this example, let's imagine we have 3 people and 3 jobs.  We represent the amount of
# money each person will produce at each job with a cost matrix.  Each row corresponds to a
# person and each column corresponds to a job.  So for example, below we are saying that
# person 0 will make $1 at job 0, $2 at job 1, and $6 at job 2.  
cost = dlib.matrix([[1, 2, 6],
                    [5, 3, 6],
                    [4, 5, 0]])


# To find out the best assignment of people to jobs we just need to call this function.
assignment = dlib.max_cost_assignment(cost)


# This prints optimal assignments:  [2, 0, 1]
# which indicates that we should assign the person from the first row of the cost matrix to
# job 2, the middle row person to job 0, and the bottom row person to job 1.
print "optimal assignments: ", assignment


# This prints optimal cost:  16.0
# which is correct since our optimal assignment is 6+5+5.
print "optimal cost: ", dlib.assignment_cost(cost, assignment)