| Summary: | 碩士 === 國立交通大學 === 應用數學系所 === 99 === This thesis considers designing efficient self-stabilizing algorithms for solving the minimal dominating set (MDS) problem. Let n denote the number of nodes in a distributed system. A self-stabilizing algorithm is said to be a t-move algorithm if when it is used, a given distributed system takes at most t moves to reach a legitimate configuration. In 2007, Turau proposed a 9n-move algorithm for the MDS problem under a distributed scheduler. Later, in 2008, Goddard et al. proposed a 5n-move algorithm for the MDS problem under a distributed scheduler. It is indeed a challenge to develop an algorithm that takes less than 5n moves under a distributed scheduler. The purpose of this thesis is to propose such an algorithm. In particular, we propose a 4n-move algorithm under a distributed scheduler; an example such that our algorithm takes 4n − 1 moves to reach a legitimate configuration has also been proposed.
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