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Christofides Algorithm
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This package(Christofides) provides a way to implement Christofides algorithm
for solving Travelling Saleman Problem(TSP) to obtain an approximate solution
on an undirected graph(Distance Matrix) provided as an upper Triangular matrix.
The Distance from a node on to itself is assumed 0.
Usage
======
Use the compute() function which takes as input a distance_matrix and returns a Christofides solution as follows::
from Christofides import christofides
TSP = christofides.compute(distance_matrix)
or::
import Christofides
TSP = Christofides.christofides.compute(distance_matrix)
The Distance Matrix is an upper Triangular matrix with distance from a node on to itself 0, since Christofides algorithm
could only be applied for undirected graphs. Also the distance between a node on to itself is practically 0.
Example for distance_matrix is as follows,
distance_matrix = ::
[[0,45,65,15],
[0,0,56,12],
[0,0,0,89],
[0,0,0,0]]
The above distance_matrix should be provided as an input to christofides.compute(), when we want to calculate TSP for
distance = ::
[[0,45,65,15],
[45,0,56,12],
[65,56,0,89],
[15,12,89,0]]
christofides.compute(distance_matrix) returns a Dictionary with following Keys:
Christofides_Solution,
Travel_Cost,
MST,
Odd_Vertices
Indexes,
Multigraph,
Euler_Tour
* Christofides_Solution: A list consisting of approximate tour for TSP.
Use: TSP['Chistofides_Solution']
* Travel_Cost: The cost of TSP tour generated.
Use: TSP['Travel_Cost']
* MST: The minimum spanning tree generated during the Christofides algorithm.
Use: TSP['MST']
* Odd_Vertices: A list of odd vertices of minimum spanning tree.
Use: TSP['Odd_Vertices']
* Indexes: List of edges from minimum cost perfect matching of odd vertices.
Use: TSP['Indexes']
* Multigraph: Edges of multigraph formed after Indexing.
Use: TSP['Multigraph']
* Euler_Tour: The Euler Tour of the Multigraph.
Use: TSP['Euler_Tour']
Support Functions in christofides
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- _csr_gen_triples(csr_matrix)
- _odd_vertices_of_MST(distance_matrix, number_of_nodes)
- min_Munkres(distance_matrix, bipartitie_graphs)
- Munkres_cost(indexes, bipartite_graph)
- bipartite_Graph(distance_matrix, bipartite_set, odd_vertices)
- create_Multigraph(distance_matrix, MST, indexes, odd_vertices)
- Euler_Tour(multigraph)
- shortcut_Euler_Tour(tour)
- cost(christofides_tour, distance_matrix)
Install
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python setup.py install
Additional Packages
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scipy, numpy, networkx, munkres
