In this paper, the naturally evolving complex systems, such as biotic and social ones, are considered. Focusing on their structures, a feature is noteworthy, i.e., the similarity in structures. The relations between t...In this paper, the naturally evolving complex systems, such as biotic and social ones, are considered. Focusing on their structures, a feature is noteworthy, i.e., the similarity in structures. The relations between the functions and behaviors of these systems and their similar structures will be studied. Owing to the management of social systems and the course of evolution of biotic systems may be regarded as control processes, the researches will be within the scope of control problems. Moreover, since it is difficult to model for biotic and social systems, it will start with the control problems of complex systems, possessing similar structures, in engineering. The obtained results show that for either linear or nonlinear systems and for a lot of control problems similar structures lead to a series of simplifications. In general, the original system may be decomposed into reduced amount of subsystems with lower dimensions and simpler structures. By virtue of such subsystems, the control problems of original system can be solved more simply. At last, it turns round to observe the biotic and social systems and some analyses are given.展开更多
反馈集问题(feedback set problem)是计算机科学中研究最为广泛和深入的图上NP完全问题之一,其在并发计算、大规模集成电路、编码设计、软件验证、社交网络分析等领域均存在重要的应用.子集反馈集问题(subset feedback set problem)是...反馈集问题(feedback set problem)是计算机科学中研究最为广泛和深入的图上NP完全问题之一,其在并发计算、大规模集成电路、编码设计、软件验证、社交网络分析等领域均存在重要的应用.子集反馈集问题(subset feedback set problem)是反馈集问题的一种更一般化的形式,更加具有普适性和实用性.近年来,这2个问题在计算复杂性上的分类工作已逐步完善,在算法领域也已出现许多重要的突破.相关研究工作分为2个部分进行介绍.第1部分详尽地介绍了反馈集和子集反馈集各种不同版本的问题,梳理了它们之间的一些重要关系,并介绍了这些问题在一般图上的计算复杂性.第2部分系统性地介绍了反馈集和子集反馈集问题在一些重要子图类上的计算复杂性,包括度有界的图类、平面图类、竞赛图图类、相交图类、禁止图图类和二部图图类.最后对反馈集和子集反馈集问题的研究现状进行分析和总结,概括了目前主流的研究趋势.展开更多
文摘In this paper, the naturally evolving complex systems, such as biotic and social ones, are considered. Focusing on their structures, a feature is noteworthy, i.e., the similarity in structures. The relations between the functions and behaviors of these systems and their similar structures will be studied. Owing to the management of social systems and the course of evolution of biotic systems may be regarded as control processes, the researches will be within the scope of control problems. Moreover, since it is difficult to model for biotic and social systems, it will start with the control problems of complex systems, possessing similar structures, in engineering. The obtained results show that for either linear or nonlinear systems and for a lot of control problems similar structures lead to a series of simplifications. In general, the original system may be decomposed into reduced amount of subsystems with lower dimensions and simpler structures. By virtue of such subsystems, the control problems of original system can be solved more simply. At last, it turns round to observe the biotic and social systems and some analyses are given.
文摘反馈集问题(feedback set problem)是计算机科学中研究最为广泛和深入的图上NP完全问题之一,其在并发计算、大规模集成电路、编码设计、软件验证、社交网络分析等领域均存在重要的应用.子集反馈集问题(subset feedback set problem)是反馈集问题的一种更一般化的形式,更加具有普适性和实用性.近年来,这2个问题在计算复杂性上的分类工作已逐步完善,在算法领域也已出现许多重要的突破.相关研究工作分为2个部分进行介绍.第1部分详尽地介绍了反馈集和子集反馈集各种不同版本的问题,梳理了它们之间的一些重要关系,并介绍了这些问题在一般图上的计算复杂性.第2部分系统性地介绍了反馈集和子集反馈集问题在一些重要子图类上的计算复杂性,包括度有界的图类、平面图类、竞赛图图类、相交图类、禁止图图类和二部图图类.最后对反馈集和子集反馈集问题的研究现状进行分析和总结,概括了目前主流的研究趋势.
