On construction of minimum energy k-fault resistant topologies

This paper studies asymmetric power assignments for various network topologies under the k-resilience 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 (k²) 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(k² + log¹⁰ n) amortized time in the plane.