1. A method implemented by a network device in a network having a plurality of nodes, the method to compute a remote loop free alternative (RLFA) next hop as a backup for a primary path next hop, where the method improves RLFA computation efficiency for a Q-Space list of nodes in a Q-space for an endpoint node by reducing calculations of a loop free condition for a path from a source node to a destination node via a tunnel between the source node and the endpoint node, where Q-space is a set of nodes from which a specific node can be reached without any path transiting a protected link or protected node, the method comprising the steps of: selecting a next candidate node having a least distance to the endpoint node or destination node from a candidate list; selecting a next neighbor node of the candidate node; adding the neighbor node to a poison list where the candidate node is in the poison list and the neighbor node is not in the candidate list, the poison list indicating that a node is not a candidate for Q-Space; and determining the Q-Space list by removing nodes from the poison list from the plurality of nodes.