A self‐stabilizing distributed algorithm for the bounded lattice domination problems under the distance‐2 model

Abstract

SummaryThe domination problem is one of the fundamental graph problems, and there are many variations. In this article, we propose a new problem called the minus ‐domination problem where , and are integers such that , , and . The problem is to assign a value from for each vertex in a graph such that the local summation of values is greater than or equal to . We also propose a framework named the bounded lattice domination for a class of domination problems, including the minus ‐domination problem. Then, we present a self‐stabilizing distributed algorithm under the distance‐2 model for the bounded lattice domination. Here, self‐stabilization is a class of fault‐tolerant distributed algorithms that tolerate transient faults. The time complexity for convergence is , where is the number of processes in a network if the cardinality of the domain of process values is finite and constant. Otherwise, the time complexity for convergence is .