Cost minimization in redundant trees for protection in vertex-redundant or edge-redundant graphs

Preplanned recovery using redundant trees in vertex-redundant or edge-redundant graphs is extended to the case where each edge has a cost and the goal is to find a pair of working and protection trees such that the cost of the working tree is as low as possible. We present efficient heuristic algorithms for this problem. Extensive computational results show that the cost of the working tree found with our algorithm is within 19% of the cost of a minimum spanning tree on the average, while the smaller cost of the working and protection trees found by the original algorithm without QoS consideration is about 95% over the cost of a minimum spanning tree on the average