The well-studied DISPERSION problem is a fundamental coordination problem in distributed robotics, where a set of mobile robots must relocate so that each occupies a distinct node of a network. DISPERSION assumes that a robot can settle at any node as long as no other robot settles on that node. In this work, we introduce LOCATION-AWARE DISPERSION, a novel generalization of DISPERSION that incorporates location awareness: Let $G = (V, E)$ be an anonymous, connected, undirected graph with $n = |V|$ nodes, each labeled with a color $\sf{col}(v) \in C = \{c_1, \dots, c_t\}, t\leq n$. A set $R = \{r_1, \dots, r_k\}$ of $k \leq n$ mobile robots is given, where each robot $r_i$ has an associated color $\mathsf{col}(r_i) \in C$. Initially placed arbitrarily on the graph, the goal is to relocate the robots so that each occupies a distinct node of the same color. When $|C|=1$, LOCATION-AWARE DISPERSION reduces to DISPERSION. There is a solution to DISPERSION in graphs with any $k\leq n$ without knowing $k,n$.
Like DISPERSION, the goal is to solve LOCATION-AWARE DISPERSION minimizing both time and memory requirement at each agent. We develop several deterministic algorithms with guaranteed bounds on both time and memory requirement. We also give an impossibility and a lower bound for any deterministic algorithm for LOCATION-AWARE DISPERSION. To the best of our knowledge, the presented results collectively establish the algorithmic feasibility of LOCATION-AWARE DISPERSION in anonymous networks and also highlight the challenges on getting an efficient solution compared to the solutions for DISPERSION.
JAIST（北陆先端科学技术大学院大学）；Kyushu University（九州大学）；Aix-Marseille University（艾克斯-马赛大学）；CNRS（法国国家科学研究中心）；University of Rome “Sapienza”（罗马第一大学）；University of Ottawa（渥太华大学）；Carleton University（卡尔顿大学）
Indian Institute of Technology Indore（印度理工学院Indore分校）；University of Illinois Chicago（伊利诺伊大学芝加哥分校）；Indian Institute of Technology Madras（印度理工学院Madras分校）；Indian Statistical Institute（印度统计研究所）；Kent State University（肯特州立大学）
Adaptive Self-Organization in Anonymous Dynamic Networks
School of Computing and Augmented Intelligence and Biodesign Center for Biocomputing, Security and Society Arizona State University（亚利桑那州立大学计算与增强智能学院及生物设计生物计算、安全与社会中心）
