Christofides Algorithm for TSP.
Project description
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
_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
python setup.py install
Additional Packages
scipy, numpy, networkx, munkres