Finding the Maximum Density Path Within Constrained Length in a Graph

Most of existing path finding problems focused on searching a path with the minimum cost, such as shortest-path length and shortest travel time. In this paper, we consider a new path finding problem, i.e., length-constrained maximum density path (LDP) problem. Given a graph with length and weight on each edge, the LDP problem aims to find the maximum density path between two nodes under a specified length constraint, where the density of the path is defined as the ratio of the path weight to the path length. To the best of our knowledge, there are no existing works that focus on this problem. We prove the problem is NP-hard. Then we propose an A*-based exact algorithm to acquire the optimal solution. Due to the expensive computational overhead of the A*-based exact algorithm, we further propose two effective approximation algorithms, i.e., the label setting algorithm and the top-k based network expansion (k-NE) algorithm. Extensive experiments on four real and synthetic datasets verify the efficiency and effectiveness of the proposed algorithms.