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This study proposes an autonomous distributed control method for single link failure based on loops in a network. This method focuses on the concept of tie-sets defined by graph theory in order to divide a network into a string of logical loops. A tie-set denotes a set of links that constitutes a loop. Based on theoretical rationale of graph theory, a string of tie-sets that cover all the nodes and links can be created by using a tree, even in an intricately-intertwined mesh network. If tie-sets are used as local management units, high-speed and stable fail-over can be realized by taking full advantage of ring-based restoration. This paper first introduces the notion of tie-sets, and then describes the distributed algorithms for link failure. Experiments are conducted against Rapid Spanning Tree Protocol (RSTP), which is generally used for fault recovery in mesh topological networks. Experimental results comparing the proposed method with RSTP suggest that our method alleviates the adverse effects of link failure with a modest increase in state information of a node.