Sometimes there are multiple shortest paths between pairs of nodes in a graph. Develop an algorithm...

 

Transcribed Image Text:

Sometimes there are multiple shortest paths between pairs of nodes in a graph. Develop an algorithm for the following task: given an undirected graph G = (V, E) with unit edge lengths and nodes v and w, output the number of distinct shortest paths from v to w. For example, for the graph below, on input v and w your algorithm should output 2. Your algorithm's running time should be linear in n = |V| and m = |E|. (a) Describe your algorithm in pseudocode. (b) Give a formal proof of correctness. (c) Show that your algorithm runs in O(n + m) time. W Sometimes there are multiple shortest paths between pairs of nodes in a graph. Develop an algorithm for the following task: given an undirected graph G = (V, E) with unit edge lengths and nodes v and w, output the number of distinct shortest paths from v to w. For example, for the graph below, on input v and w your algorithm should output 2. Your algorithm's running time should be linear in n = |V| and m = |E|. (a) Describe your algorithm in pseudocode. (b) Give a formal proof of correctness. (c) Show that your algorithm runs in O(n + m) time. W Sometimes there are multiple shortest paths between pairs of nodes in a graph. Develop an algorithm for the following task: given an undirected graph G = (V, E) with unit edge lengths and nodes v and w, output the number of distinct shortest paths from v to w. For example, for the graph below, on input v and w your algorithm should output 2. Your algorithm's running time should be linear in n = |V| and m = |E|. (a) Describe your algorithm in pseudocode. (b) Give a formal proof of correctness. (c) Show that your algorithm runs in O(n + m) time. W

Answer rating: 100% (QA)

Introduction is given below Explanation To finding the shortest path between two nodes is a common problem However in some cases there can be multiple ... View the full answer