Quality-of-service and quality-of-protection issues in preplanned recovery schemes using redundant trees

We study quality-of-service (QoS) and quality-of-protection (QoP) issues in redundant tree based preplanned recovery schemes for a single-link failure in two-edge connected graphs and for a single-node failure in two-connected graphs. We present schemes (to be called G-MFBG schemes) that generalize the schemes (to be called MFBG schemes) developed by Me´dard et al. (1997) to construct a pair of redundant trees, called red and blue trees, which guarantees fast recovery from any single-link/node failure, as long as the failed node is not the root node. Using the G-MFBG schemes, we study QoS issues relating to red/blue trees. We present effective heuristics for computing a pair of redundant trees with low average delay or small total cost. We develop an optimal algorithm for computing a pair of red/blue trees with maximum bandwidth. Furthermore, a pair of red/blue trees guarantees fast recovery from simultaneous multiple failures if it satisfies certain properties. This leads us to define the concept of QoP of a pair of red/blue trees. We present an effective heuristic to construct a pair of red/blue trees with high QoP. The paper concludes with a discussion of computational results that demonstrate the effectiveness of the different algorithms presented.