Finding top-k shortest paths with diversity

The classical K Shortest Paths (KSP) problem, which identifies the k shortest paths in a directed graph, plays an important role in many application domains, such as providing alternative paths for vehicle routing services. However, the returned k shortest paths may be highly similar, i.e., sharing significant amounts of edges, thus adversely affecting service qualities. In this paper, we formalize the K Shortest Paths with Diversity (KSPD) problem that identifies top-k shortest paths such that the paths are dissimilar with each other and the total length of the paths is minimized. We first prove that the KSPD problem is NP-hard and then propose a generic greedy framework to solve the KSPD problem in the sense that (1) it supports a wide variety of path similarity metrics which are widely adopted in the literature and (2) it is also able to efficiently solve the traditional KSP problem if no path similarity metric is specified. The core of the framework includes the use of two judiciously designed lower bounds, where one is dependent on and the other one is independent on the chosen path similarity metric, which effectively reduces the search space and significantly improves efficiency. Empirical studies on five real-world and synthetic graphs and five different path similarity metrics offer insight into the design properties of the proposed general framework and offer evidence that the proposed lower bounds are effective.