Efficient Algorithms for Distance Problems in Large Networks

大型网络中距离问题的高效算法

• 批准号: RGPIN-2018-04607
• 负责人: Gu, Qianping
• 金额: $ 1.68万
• 依托单位: Simon Fraser University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2020
• 资助国家: 加拿大
• 起止时间: 2020-01-01 至 2021-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=713165
• 关键词: Efficient; Algorithms; Distance; Problems; Large

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.

图中的最短距离/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。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等新的应用期望在大型网络中获得距离查询的真实的时间响应。经典的最短路径算法对于这些新的挑战是低效的，这些新的挑战近来受到了广泛的关注。一个主要的方法来解决新的挑战是开发两个阶段的算法，预先计算一些距离信息，并保持在一个数据结构，称为Oracle的信息，在第一阶段和回答距离查询的协助下，在第二阶段的Oracle。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。一个两阶段的算法，具有较小的查询时间和oracle大小的广泛的应用是非常重要的，以应对新的挑战。已经开发了大量的两阶段算法。然而，这些算法存在局限性：它们的Oracle大小对于大型网络中的新应用程序来说太大;大多数算法都很复杂，难以实现，使得它们只在理论上有趣。本研究的目标是开发新的两阶段算法，这是简单，易于实现，并具有小的查询时间和预言机大小在理论和实践中的大型网络，如交通网络，计算机网络和复杂的社交网络的新应用。