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  and  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.
- Energy-efficient design
- Wireless ad hoc networks
ASJC Scopus subject areas
- Hardware and Architecture
- Computer Networks and Communications