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We propose a novel dynamic shared-path protection (DSPP) algorithm, called DSPP-SRLG, based on shared risk link group (SRLG) constraints to protect completely multi-link failures of a single SRLG breakdown for WDM mesh networks. DSPP-SRLG can dynamically adjust the link-cost according to the current state of the network and search a primary path and a SRLG-disjoint backup path for each connection request. If two primary paths are SRLG-disjoint, then their corresponding backup paths can share the common resources. Simulation results show that not only can DSPP-SRLG completely protect multi-link failures of the single SRLG breakdown but can it also make tradeoffs between the resource utilization ratio (or blocking ratio) and the protection-switching time.