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/INSTALLING THE DLIB PYTHON INTERFACE
#   You can install dlib using the command:
#       pip install dlib
#
#   Alternatively, if you want to compile dlib yourself then go into the dlib
#   root folder and run:
#       python setup.py install
#   or
#       python setup.py install --yes USE_AVX_INSTRUCTIONS
#   if you have a CPU that supports AVX instructions, since this makes some
#   things run faster.  
#
#   Compiling dlib 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: {}".format(assignment))

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