The Impact of Information in Distributed Submodular Maximization

作     者：Grimsman, David Ali, Mohd Shabbir Hespanha, Joao P. Marden, Jason R. 

作者机构：Univ Calif Santa Barbara Dept Elect & Comp Engn Santa Barbara CA 93106 USA Orange Labs F-75001 Paris France 

出 版 物：《IEEE TRANSACTIONS ON CONTROL OF NETWORK SYSTEMS》 (IEEE Trans. Control Netw. Syst.)

年 卷 期：2019年第6卷第4期

页      面：1334-1343页

核心收录：

学科分类：0808[工学-电气工程] 08[工学] 0811[工学-控制科学与工程] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

基　　金：ONR [N00014-17-1-2060, N00014-16-1-2710] NSF [ECCS-1638214, ECCS-1608880] NetLearn ANR project [ANR-13-INFR-004] 

主　　题：Distributed algorithms graph theory greedy algorithms multiagent systems optimization 

摘      要：The maximization of submodular functions is an NP-Hard problem for certain subclasses of functions, for which a simple greedy algorithm has been shown to guarantee a solution whose quality is within 1/2 of the optimal. When this algorithm is implemented in a distributed way, agents sequentially make decisions based on the decisions of all previous agents. This work explores how limited access to the decisions of previous agents affects the quality of the solution of the greedy algorithm. Specifically, we provide tight upper and lower bounds on how well the algorithm performs, as a function of the information available to each agent. Intuitively, the results show that performance roughly degrades proportionally to the size of the largest group of agents that make decisions independently. Additionally, we consider the case where a system designer is given a set of agents and a global limit on the amount of information that can be accessed. Our results show that the best designs partition the agents into equally sized sets and allow agents to access the decisions of all previous agents within the same set.