Linear time construction of redundant trees for recovery schemes enhancing QoP and QoS

Medard, Finn, Barry and Gallager proposed an elegant recovery scheme (known as the MFBG scheme) using redundant trees. Xue, Chen and Thulasiraman extended the MFBG scheme and introduced the concept of quality of protection (QoP) as a metric of multifailure recovery capabilities for single failure recovery schemes. In this paper, we present three linear time algorithms for constructing redundant trees for single link failure recovery in 2-edge connected graphs and for single node failure recovery in 2-connected graphs. Our first algorithm aims at high QoP for single link recovery schemes in 2-edge connected graphs. The previous best algorithm has a running time of O(n²(m+n)), where n and m are the number of nodes and links in the network. Our algorithm has a running time of O(m+n), with comparable performance. Our second algorithm aims at high QoS for single link recovery schemes in 2-edge connected graphs. Our algorithm improves the previous best algorithm with O(n²(m+n)) time complexity to O(m+n) time complexity with comparable performance. Our third algorithm aims at high QoS for single node recovery schemes in 2-connected graphs. Again, our algorithm improves the previous best algorithm with O(n²(m+n)) time complexity to O(m+n) time complexity with comparable performance. Simulation results show that our new algorithms outperform previously known linear time algorithms significantly in terms of QoP or QoS, and outperform other known algorithms in terms of running time, with comparable QoP of QoS performance.