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In this paper, we define a new concept neighborhood mutual remainder (NMR). An NMR distributed algorithms should satisfy global fairness, l-exclusion and repeated local rendezvous requirements. We give a simple self-stabilizing algorithm to demonstrate the design paradigm to achieve NMR, and also present applications of NMR to a Look-Compute-Move robot system.doi:10.4230/lipics.disc.2019.43 dblp:conf/wdag/DolevKKOW19 fatcat:p3j6kgu2anhwjgu7sni4w7gg2y