In the past couple of decades, graphs have been widely used to model complex relationships among various entities in real applications. Shortest path query is a fundamental problem in graphs and has been well-studied. Most existing approaches for the shortest path problem consider that there is only one kind of cost in networks. However, there always are several kinds of cost in networks and users prefer to select an optimal path under the global consideration of these kinds of cost. In this paper, we study the problem of finding the optimal path in the multi-cost networks. We prove this problem is NP-hard and the existing index techniques cannot be used to this problem. We propose a novel partition-based index with contour skyline techniques to find the optimal path. We propose a vertex-filtering algorithm to facilitate the query processing. We conduct extensive experiments on six real-life networks and the experimental results show that our method has an improvement in efficiency by an order of magnitude compared to the previous heuristic algorithms.

在过去的几十年中，图已被广泛用于在实际应用中为各种实体之间的复杂关系建模。最短路径查询是图形中的一个基本问题，并且已经过深入研究。对于最短路径问题，大多数现有方法都认为网络中只有一种成本。然而，网络中总是存在几种成本，并且用户倾向于在全局考虑这些成本的情况下选择最佳路径。在本文中，我们研究了在多成本网络中寻找最优路径的问题。我们证明此问题是NP难题，并且现有索引技术无法用于此问题。我们提出了一种新的基于分区的索引，并使用轮廓天际线技术来找到最佳路径。我们提出一种顶点过滤算法，以方便查询处理。