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Abstract-As a generalization of the traditional path protection scheme in WDM networks where a backup path is needed for each active path, the partial path protection scheme uses a collection of backup paths to protect an active path, where each backup path in the collection protects one or more links on the active path such that every link on the active path is protected by one of the backup paths. While there is no known polynomial time algorithm for computing an active path and a corresponding backup path using the path protection scheme for a given source-destination node pair, we show that an active path and a corresponding collection of backup paths using the partial path protection scheme can be computed in polynomial time, whenever they exist, under each of the following two network models: (a) dedicated protection in WDM networks without wavelength converters; and (b) shared protection in WDM networks without wavelength converters. Under each of the two models, we prove that for any given source s and destination d in the network, if one candidate active path connecting s and d is protectable using partial path protection, then any candidate active path connecting s and d is also protectable using partial path protection. This fundamental property leads to efficient shortest active path algorithms that can find an active path and its corresponding partial path protections whenever they exist. Simulation results show that shared partial path protection outperforms shared path protection in terms of blocking probability.

Abstract-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

Broadcasting and multicasting packets in a power efficient way is a critical task in wireless ad hoc networks. In a recent paper [6], Li et al. study the Minimum Energy Broadcast (MEB) routing problem in a wireless ad hoc network where every node has an omni-directional antenna and a fixed transmission power level. We extend their work to wireless networks with directional antennas in this paper. We formulate the Minimum Power Multicasting/Broadcasting using Directional Antennas (PMDA/PBDA) problems. For each problem, we present an approximation algorithm with worstcase approximation ratio O(log 2 n), where n is the number of nodes in the network. We also present several effective heuristics to solve the problems, the Shortest Path Tree (SPT) heuristic, the Directed Minimum Spanning Tree (DMST) heuristic and a greedy heuristic. Simulation results are presented to show the performance of our algorithms.