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We first define in mathematics\nthe maximum extent of resource sharing for a protection path given the\ncorresponding working path according to the current network link-state.\nThen the problem of solving the least-cost Working & protection\npath-pair (in terms of the sum of the cost) is formulated into an\nInteger Linear Programming process. Due to the dependency of the\nprotection path on its working path, however, I the formulation is not\nscalable with the network size, and takes an: extra effort to solve.\nTherefore, we introduce two heuristic algorithms, called Iterative\nTwo-Step-Approach (ITSA) & Maximum Likelihood Relaxation (MLR), which\naim to explore the approximating optimal solutions with less\ncomputation time. We evaluate the performance of the proposed schemes,\nand make a comparison with some reported counterparts. The simulation\nresults show that the ITSA scheme, with a properly defined tolerance to\noptimality, can achieve the best performance at the expense of more\ncomputation time. 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