The paradigm of self-stabilization provides a mechanism to design efficient localized distributed algorithms that are proving to be essential for modern day large networks of sensors. We provide self-stabilizing algorithms (in the shared-variable ID-based model) for three graph optimization problems: a minimal total dominating set (where every node must be adjacent to a node in the set) and its generalizations, a maximal k-packing (a set of nodes where every pair of nodes are more than distance

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... k apart), and a maximal strong matching (a collection of totally disjoint edges).