The Ripple-Spreading Algorithm for Many-to-Many the k Shortest Path Problem

Reference: Hu X B, Zhang C, Zhang G P, et al. Finding the k shortest paths by ripple-spreading algorithms[J]. Engineering Applications of Artificial Intelligence, 2020, 87: 103229.

Variables	Meaning
network	Dictionary, {node 1: {node 2: [weight 1, weight 2, ...], ...}, ...}
new_network	The inversed network
source	List, the source nodes
destination	List, the destination nodes
k	The k shortest paths
nn	The number of nodes
neighbor	Dictionary, {node1: [the neighbor nodes of node1], ...}
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]
omega	Dictionary, omega[n] contains all ripples generated at node n

Example

The source nodes are 0 and 1, and the destination nodes are 10 and 11. The aim is to determine the three shortest paths from every source node to destination nodes.

if __name__ == '__main__':
    network = {
        0: {1: 6, 2: 7, 3: 4},
        1: {0: 6, 3: 3, 4: 7},
        2: {0: 7, 5: 2, 7: 5},
        3: {0: 4, 1: 3, 5: 2, 6: 9},
        4: {1: 7, 6: 7, 9: 9},
        5: {2: 2, 3: 2, 7: 6, 8: 4},
        6: {3: 9, 4: 7, 8: 7, 9: 4},
        7: {2: 5, 5: 6, 10: 3},
        8: {5: 4, 6: 7, 10: 5, 11: 1},
        9: {4: 9, 6: 4, 11: 7},
        10: {7: 3, 8: 5, 11: 7},
        11: {8: 1, 9: 7, 10: 7}
    }
    source = [0, 1]
    destination = [10, 11]
    k = 3
    print(main(network, source, destination, k))

Output:

{
    0: [
        {'path': [0, 3, 5, 8, 11], 'length': 11}, 
        {'path': [0, 2, 5, 8, 11], 'length': 14}, 
        {'path': [0, 2, 7, 10], 'length': 15},
    ], 
    1: [
        {'path': [1, 3, 5, 8, 11], 'length': 10}, 
        {'path': [1, 3, 5, 7, 10], 'length': 14}, 
        {'path': [1, 3, 5, 8, 10], 'length': 14},
    ]
}

The shortest paths from node 0 are 0->3->5->8->11, 0->2->5->8->11, and 0->2->7->10.

The shortest paths from node 1 are 1->3->5->8->11, 1->3->5->7->11, and 1->3->5->8->10.