Efficient Algorithms for Distance Problems in Large Networks

图的最短距离/路径问题是计算机算法中最基本的问题之一，在交通、社会和信息网络等领域有着广泛的应用。诸如地理信息系统、智能交通系统、社会网络分析系统和计算机网络管理系统中的新应用期望对大型网络中的距离查询获得实时答案。传统的最短路径算法在应对这些新的挑战时效率低下，近年来受到了广泛关注。解决新挑战的一个主要方法是开发两阶段算法，在第一阶段预先计算一些距离信息，并将信息保存在称为Oracle的数据结构中，在第二阶段在Oracle的帮助下回答距离查询。查询时间(第二阶段的时间)和Oracle大小(Oracle所需的内存空间)是评估算法的主要标准。一种具有较小查询时间和较大Oracle大小的两阶段算法对于应对新的挑战具有重要意义。已有大量的两阶段算法被开发出来。然而，这些算法也有局限性：它们的先知大小对于大型网络中的新应用来说太大了；大多数算法都很复杂，很难实现，使得它们只在理论上有趣。本研究的目标是为交通网络、计算机网络和复杂社会网络等大型网络中的新应用开发简单、易于实现、查询时间和Oracle大小都较小的两阶段算法。

The shortest distance/path problems in graphs are among the most fundamental problems in computer algorithms and have numerous applications in areas such as transportation, social and information networks. New applications such as those in Geographic Information Systems, intelligent transportation systems, social network analysis systems, and computer network management systems expect to get a real time answer for a distance query in large networks. Classical shortest path algorithms are inefficient for these new challenges which have received much attention recently. A major approach to address the new challenges is to develop two-phase algorithms which pre-compute some distance information and keep the information in a data structure, called oracle, in phase one and answer distance queries with the assistance of the oracle in phase two. The query time (time in phase two) and oracle size (memory space required by the oracle) are major criteria for evaluating the algorithms. A two-phase algorithm with a small query time and oracle size for a wide range of applications is of great importance to address the new challenges. A large number of two-phase algorithms have been developed. However there are limitations in these algorithms: their oracle sizes are too large for new applications in large networks; most algorithms are complex and difficult to implement, making them only theoretically interesting. The goals of this research are to develop new two-phase algorithms which are simple and easy to implement, and have small query time and oracle size in both theory and practice for new applications in large networks such as transportation networks, computer networks and complex social networks.**