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In optical metro-aggregation networks, logical partitioning or network slicing can enforce the high reliability required by advanced services. This can be achieved by enabling flexible resource management. Virtual network functions composing a slice can be deployed over physical nodes using different strategies. In reliable network slicing, a virtual network request involves allocating link-disjoint primary and backup resources to protect against single link failure. In this paper, we present a reliable virtual network embedding algorithm over elastic optical networks considering shared link protection (SLP). This is to reduce the required backup resources. We propose a heuristic SLP mapping algorithm that enables the multiplexing of S primary links to share the same backup resource on a given backup link, offering improved resource utilization. We extend our proposed SLP algorithm to be represented by mapping matrices. These matrices define the mapping of S sharing links on a physical link as well as the required sharing capacity. SLP is shown to perform remarkably better than dedicated link protection and allows efficient wavelength channel utilization by reducing the backup resources needed for protection by up to 37%.