We consider the problem of finding a maximal independent set (MIS) of an unknown graph by mobile agents. Let n agents be initially positioned arbitrarily at the nodes of an anonymous graph \(G=(V,E)\) . The agents reposition themselves to achieve a configuration that forms an MIS of the graph, and terminate. Our algorithm solves the problem and achieves termination in \(O(max\{n\log ^2 n, m\})\) rounds utilizing \(O(\log n)\) memory per agent. The agents do not have any prior knowledge of any graph parameters. Additionally, we solve the leader election problem during the process. From the MIS perspective, our result improves over Pattanayak et al. (ICDCN 2024) by removing global knowledge as well as by reducing run time. We improve over Kshemkalyani et al. (DISC 2024) by reducing memory requirement as well as runtime. This is because authors provide a runtime of \(O(n\Delta )\) where \(\Delta \) is the maximum degree of the graph and it can be asymptotically more than our runtime whenever the average degree is much lesser than the maximum degree. Due to the same reasoning our time complexity is better compared to the runtime of MIS finding in Kshemkalyani et al. (AAMAS 2025) as well.
