Distributed Algorithm for Shortest Path Problem in Undirected Graphs via Randomized Strategy

In this paper, we introduce a distributed algorithm for single source shortest path problem for undirected graphs. In this problem, we find the shortest path from a given source node to other nodes in the graph. We start with undirected unweighted graphs in which the shortest path is a path with minimum number of edges. Following, we modify the algorithm to find shortest path for weighted graphs in which the shortest path is a path with minimum cost, i.e., sum of the edge weights. We examine the convergence time of the random algorithm for random Erdos-Renyi graphs as a random variable; based on that we approximate the stop-time criteria of the algorithm for graphs with unknown topology. We claim that the stop-time criteria is related to the graph parameters such as number of nodes and graph diameter.