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In this paper, we investigate the problem of dynamic survivable routing in wavelength-division-multiplexing optical networks and propose a new path-protection algorithm called Enhanced Shared Backup Paths Protection (ESBPP) to provide the complete survivability for double-link failures. In order to improve the resource-utilization ratio, we present the new rule of sharing backup resources that can yield better resource-utilization ratio than previous methods. In order to overcome the problem of trap paths, we develop a new routing method to find the feasible solution with three link-disjoint paths for each connection request. Compared to previous algorithms for double-link failures, ESBPP can obtain higher resource-utilization ratio and lower blocking probability.