# Probabilistic shortest path routing algorithm for optical networks

Data transfer operations is a crucial aspect in case of networking and routing. So efficient data transfer operations is a must need, with minimum hardware cost (Optical Cables, WDM Network components, Decoders, Multiplexers) and also in the minimum time possible. Thus, the need is to propose an algorithm that finds the shortest path between two nodes (source node and destination node).

Let’s see a completely new algorithm unlike Dijkstra’s Shortest Path or any other algorithm for finding Shortest Path.

Given a graph and two nodes (source node and destination node), find the shortest path between them.

Let’s Calculate the distance ratio for each link :

Distance of link AB [denoted by

`d(AB)`

] = 10

Distance of link AC [denoted by`d(AC)`

] = 12For link

AB, Distance Ratio of AB = d(AB) / (d(AB) + d(AC))

For linkAC, Distance Ratio of AC = d(AC) / (d(AB) + d(AC))

**Algorithm :**

Given a graph and two nodes - 1. Find all the paths connecting the two nodes. 2. For each path calculate probability = (Distance Ratio). 3. After looping over all such paths, find the path for which the probability turns out to be minimum.

Examples :

Input :Output :Shortest Path is [A -> B]Explanation :All possible paths are P1 = [A->B] P2 = [A->C->B] P3 = [A->D->B] total distance D = d(P1) + d(P2) + d(P3) = (3) + (2 + 5) + (4 + 3) = 17 distance ratio for P1 = d(P1) / D = 3/17 distance ratio for P2 = d(P2) / D = 7/17 distance ratio for P3 = d(P3) / D = 7/17 So the shortest path is P1 = [A->B]

Input :Output :Shortest Path is [A -> B]

Let’s illustrate the algorithm with a 7-node network and find out the Probabilistic shortest path between `node 1`

and `node 5`

.

Below is the implementation :

`# Python program to find Probabilistic ` `# shortest path routing algorithm for ` `# optical networks ` ` ` `# importing random module ` `import` `random ` ` ` `# Number of nodes ` `NODES ` `=` `7` ` ` `# very small invalid ` `# when no link exists ` `INVALID ` `=` `0.001` ` ` ` ` `distance_links ` `=` `[[INVALID ` `for` `i ` `in` `range` `(NODES)] ` ` ` `for` `j ` `in` `range` `(NODES)] ` `# distance of each link ` `distance_links[` `0` `][` `1` `] ` `=` `7` `distance_links[` `1` `][` `0` `] ` `=` `7` `distance_links[` `1` `][` `2` `] ` `=` `8` `distance_links[` `2` `][` `1` `] ` `=` `8` `distance_links[` `0` `][` `2` `] ` `=` `9` `distance_links[` `2` `][` `0` `] ` `=` `9` `distance_links[` `3` `][` `0` `] ` `=` `9` `distance_links[` `0` `][` `3` `] ` `=` `9` `distance_links[` `4` `][` `3` `] ` `=` `4` `distance_links[` `3` `][` `4` `] ` `=` `4` `distance_links[` `5` `][` `4` `] ` `=` `6` `distance_links[` `4` `][` `5` `] ` `=` `6` `distance_links[` `5` `][` `2` `] ` `=` `4` `distance_links[` `2` `][` `5` `] ` `=` `4` `distance_links[` `4` `][` `6` `] ` `=` `8` `distance_links[` `6` `][` `4` `] ` `=` `8` `distance_links[` `0` `][` `6` `] ` `=` `5` `distance_links[` `6` `][` `0` `] ` `=` `5` ` ` ` ` ` ` `# Finds next node from current node ` `def` `next_node(s): ` ` ` `nxt ` `=` `[] ` ` ` ` ` `for` `i ` `in` `range` `(NODES): ` ` ` `if` `(distance_links[s][i] !` `=` `INVALID): ` ` ` `nxt.append(i) ` ` ` `return` `nxt ` ` ` `# Find simple paths for each ` `def` `find_simple_paths(start, end): ` ` ` `visited ` `=` `set` `() ` ` ` `visited.add(start) ` ` ` ` ` `nodestack ` `=` `list` `() ` ` ` `indexstack ` `=` `list` `() ` ` ` `current ` `=` `start ` ` ` `i ` `=` `0` ` ` ` ` `while` `True` `: ` ` ` ` ` `# get a list of the neighbors ` ` ` `# of the current node ` ` ` `neighbors ` `=` `next_node(current) ` ` ` ` ` `# Find the next unvisited neighbor ` ` ` `# of this node, if any ` ` ` `while` `i < ` `len` `(neighbors) ` `and` `neighbors[i] ` `in` `visited: ` ` ` `i ` `+` `=` `1` ` ` ` ` `if` `i >` `=` `len` `(neighbors): ` ` ` `visited.remove(current) ` ` ` ` ` `if` `len` `(nodestack) < ` `1` `: ` ` ` `break` ` ` ` ` `current ` `=` `nodestack.pop() ` ` ` `i ` `=` `indexstack.pop() ` ` ` ` ` `elif` `neighbors[i] ` `=` `=` `end: ` ` ` `yield` `nodestack ` `+` `[current, end] ` ` ` `i ` `+` `=` `1` ` ` ` ` `else` `: ` ` ` `nodestack.append(current) ` ` ` `indexstack.append(i ` `+` `1` `) ` ` ` `visited.add(neighbors[i]) ` ` ` `current ` `=` `neighbors[i] ` ` ` `i ` `=` `0` ` ` `# Find the shortest path ` `def` `solution(sour, dest): ` ` ` ` ` `block ` `=` `0` ` ` `l ` `=` `[] ` ` ` `for` `path ` `in` `find_simple_paths(sour, dest): ` ` ` `l.append(path) ` ` ` ` ` `k ` `=` `0` ` ` `for` `i ` `in` `range` `(` `len` `(l)): ` ` ` `su ` `=` `0` ` ` `for` `j ` `in` `range` `(` `1` `, ` `len` `(l[i])): ` ` ` `su ` `+` `=` `(distance_links[l[i][j` `-` `1` `]] ` ` ` `[l[i][j]]) ` ` ` `k ` `+` `=` `su ` ` ` ` ` `# print k ` ` ` `dist_prob ` `=` `[] ` ` ` `probability ` `=` `[] ` ` ` ` ` `for` `i ` `in` `range` `(` `len` `(l)): ` ` ` `s, su ` `=` `0` `, ` `0` ` ` ` ` `for` `j ` `in` `range` `(` `1` `, ` `len` `(l[i])): ` ` ` ` ` `su ` `+` `=` `(distance_links[l[i][j` `-` `1` `]] ` ` ` `[l[i][j]]) ` ` ` ` ` `dist_prob.append(su` `/` `(` `1.0` `*` `k)) ` ` ` ` ` ` ` `for` `m ` `in` `range` `(` `len` `(dist_prob)): ` ` ` `z ` `=` `(dist_prob[m]) ` ` ` `probability.append(z) ` ` ` ` ` `for` `i ` `in` `range` `(` `len` `(probability)): ` ` ` `if` `(probability[i] ` `=` `=` `min` `(probability)): ` ` ` ` ` `z ` `=` `l[i] ` ` ` `print` `(` `"Shortest Path is"` `, end ` `=` `" "` `) ` ` ` `print` `(z) ` ` ` `# Driver Code ` `if` `__name__ ` `=` `=` `'__main__'` `: ` ` ` `source, dest ` `=` `1` `, ` `5` ` ` ` ` `# Calling the solution function ` ` ` `solution(source, dest) ` |

*chevron_right*

*filter_none*

Output :

Shortest Path is [1, 2, 5]

**Advantage over common Shortest Path Algorithms :**

Most of the shortest path algorithms are greedy algorithms. So its based on the fact that an optimal solution leads to a globally optimal solution. In most of the cases, due to greedy property, it may not always lead to an optimal solution. But using this algorithm, one can always guarantee an optimal solution and hence the accuracy is 100%.

## Recommended Posts:

- Dijkstra’s shortest path algorithm using set in STL
- Dijkstra's Shortest Path Algorithm using priority_queue of STL
- Dijkstra's shortest path algorithm | Greedy Algo-7
- Printing Paths in Dijkstra's Shortest Path Algorithm
- Dijkstra's shortest path algorithm in Java using PriorityQueue
- Open shortest path first (OSPF) - Set 2
- Some interesting shortest path questions | Set 1
- Shortest path in a Binary Maze
- Dijkstra's shortest path with minimum edges
- Shortest Path in Directed Acyclic Graph
- 0-1 BFS (Shortest Path in a Binary Weight Graph)
- Open Shortest Path First (OSPF) Protocol fundamentals
- Shortest path with exactly k edges in a directed and weighted graph
- Open Shortest Path First (OSPF) protocol States
- Multi Source Shortest Path in Unweighted Graph

If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.