A self‐stabilizing distributed algorithm for the 1‐MIS problem under the distance‐3 model

Summary Fault‐tolerance and self‐organization are critical properties in modern distributed systems. Self‐stabilization is a class of fault‐tolerant distributed algorithms which has the ability to recover from any kind and any finite number of transient faults and topology changes. In this article, we propose a self‐stabilizing distributed algorithm for the 1‐MIS problem under the unfair central daemon assuming the distance‐3 model. Here, in the distance‐3 model, each process can refer to the values of local variables of processes within three hops. Intuitively speaking, the 1‐MIS problem is a variant of the maximal independent set (MIS) problem with improved local optimizations. The time complexity (convergence time) of our algorithm is O(n)$$ O(n) $$ steps and the space complexity is O(logn)$$ O\left(\log n\right) $$ bits, where n$$ n $$ is the number of processes. Finally, we extend the notion of 1‐MIS to p$$ p $$‐MIS for each nonnegative integer p$$ p $$, and compare the set sizes of p$$ p $$‐MIS (p=0,1,2,…$$ p=0,1,2,\dots $$) and the maximum independent set.