On construction of minimum energy k-fault resistant topologies

This paper studies asymmetric power assignments for various network topologies under the kresilience criterion in static and dynamic geometric settings. We aim to minimize the total energy consumption, which is usually NP-hard for a desired link topology. We develop a general approximation framework for various topology control problems under the k-fault resilience criterion in the plane. We use it to obtain an O(k) approximation ratio for three k-fault resistant topology control problems: multicast, broadcast and convergecast. To the best of our knowledge, these are the first non-trivial results for these problems. In addition we present interesting results for the linear case of k-multicast, k-broadcast and k-convergecast. We also extend our static algorithms for k-strong connectivity in [15] and [41] to support dynamic node insert/delete operations in O(log n) time for the linear case and an expected O(k poly log n) amortized time in the plane.