Dynamic Graph Shortest Path Algorithm

Abstract

Shortest paths computation in graph is one of the most fundamental operation in many applications such as social network and sensor network. When a large graph is updated with small changes, it is really expensive to recompute the new shortest path via the traditional static algorithms. To address this problem, dynamic algorithm that computes the shortest-path in response to updates is in demand. In this paper, we focus on dynamic algorithms for shortest point-to-point paths computation in directed graphs with positive edge weights. We develop novel algorithms to handle the single-edge updating and the batch edge updating. We prove that our algorithms can compute the shortest paths for updated graph in time polynomial to the size of updated part of the graph. We experimentally verify that these dynamic algorithms significantly outperform their batch counterparts in response to small changes, using real-life data and synthetic data.