The Ripple-Spreading Algorithm for the $k$-Color Shortest Path Problem

Reference: Y.M. Ma, H. Zhou, X.B. Hu. The ripple-spreading algorithm for the k-color shortest path problem[C]//2022 IEEE Symposium Series on Computational Intelligence (SSCI). IEEE.

The $k$-color shortest path problem ($k$-CSPP) aims to find the shortest path that traverses at most $k$ colors on edge-colored graphs.

Variables	Meaning
network	{node 1: {node 2: [length, color], ...}, ...}
source	The source node
destination	The destination node
k	The maximum number of colors traversed by the path
nn	The number of nodes
neighbor	Dictionary, [[the neighbor nodes of node 1], [the neighbor nodes of node 2], ...]
v	The ripple-spreading speed (i.e., the minimum length of arcs)
t	The simulated time index
nr	The number of ripples - 1
epicenter_set	List, the epicenter node of the i-th ripple is epicenter_set[i]
path_set	List, the path of the i-th ripple from the source node to node i is path_set[i]
radius_set	List, the radius of the i-th ripple is radius_set[i]
active_set	List, active_set contains all active ripples
objective_set	List, the objective value of the traveling path of the i-th ripple is objective_set[i]
color_set	List, the colors traversed by the traveling path of the i-th ripple is color_set[i]
omega	Dictionary, omega[n] = i denotes that ripple i is generated at node n

Example

if __name__ == '__main__':
    # The color: 1 denotes black, 2 denotes red, 3 denotes blue, and 4 denotes green.
    temp_network = {
        0: {1: [1, 1], 3: [1, 4]},
        1: {2: [1, 2], 4: [1, 3]},
        2: {5: [1, 3]},
        3: {6: [1, 1]},
        4: {3: [1, 1], 7: [1, 4]},
        5: {4: [1, 1], 8: [1, 4]},
        6: {7: [1, 3]},
        7: {8: [1, 2]},
        8: {}
    }
    source_node = 0
    destination_node = 8
    color_num = 3
    print(main(temp_network, source_node, destination_node, color_num))

Output:

{
    'path': [0, 1, 4, 3, 6, 7, 8], 
    'color': {1, 2, 3}, 
    'length': 6,
}