Combinatorial Algorithms for Parallel and Distributed Computing

拟议的研究计划将研究并行和分布式计算的计算机系统中的通信问题。为了在静态和动态图形中实现快速高效的通信，将对组合算法进行设计和分析。在静态网络中，将考虑不同的并行和分布式原语，如广播、多播、八卦。在动态图中，将研究最快、最短和最重要的广播问题。通过对每个处理器可用的信息量、发送者和接收者的数量、消息的长度、传输或处理延迟、故障链路的数量、消息的数量等施加约束来考虑各种信息传播模型。这些原语，尤其是广播和多播，在并行处理、数据迁移、高速缓存一致性和通信网络中的数据共享中发挥重要作用。广播时间是衡量网络整体性能的主要指标之一。这些原语不仅在大规模复杂网络、并行机中很重要，而且在工作站网络中也很重要。在最近建立的称为时态图或时态网络的研究领域中，基于图的动态性质来考虑不同的基本通信问题。网络中跳数最少的通信称为最短广播(或简称最短广播)。消息到达时间最早的通信称为最早广播(简称最早广播)，持续时间最短的通信称为最快广播(简称最快广播)。所有这些以及在不同假设下时态图中的一些更基本的图论参数将被研究。

The proposed research program will investigate communication problems in computer systems for parallel and distributed computing. To achieve fast and efficient communication in static and dynamic graphs combinatorial algorithms will be designed and analyzed. In static networks different parallel and distributed primitives such as broadcasting, multicasting, gossiping will be considered. In dynamic graphs fastest, shortest and foremost broadcast problems will be investigated. Various information dissemination models are considered by placing constraints on the amount of information available for each processor, number of senders and receivers, length of the message, transmission or processing delay, the number of faulty links, the number of messages, etc. These primitives, especially broadcasting and multicasting, play an important role in parallel processes, in data migration, in cache coherence and in data sharing in communication networks. Broadcast time is one of the main measures of overall network performance. These primitives are also important not only in massively complex networks, parallel machines but also in networks of workstations. In a recently established research area, called temporal graphs or temporal networks, different basic communication problems are considered based on the dynamic nature of the graph. Communication with minimum number of hops in the network is called shortest broadcast (or shortly shortestcast). Communication with earliest arrival time of the message is called foremost broadcast (shortly foremostcast), and communication with smallest duration is called fastest broadcast (shortly fastestcast). All these and some even more fundamental graph theoretic parameters in temporal graphs under different assumptions will be investigated.