Local approximation schemes for topology control
Mirela Damian, Saurav Pandit, Sriram V. Pemmaraju · 2006
This paper presents a distributed algorithm for wireless ad-hoc networks that runs in polylogarithmic number of rounds in the size of the network and constructs a lightweight, linear size, (1+ε)-spanner for any given ε> 0. A wireless network is modeled by a d-dimensional α-quasi unit ball graph (α-UBG), which is a higher dimensional generalization of the standard unit disk graph (UDG) model. The d-dimensional α-UBG model goes beyond the unrealistic “flat world ” as-sumption of UDGs and also takes into account transmission errors, fading signal strength, and physical obstructions. The main result in the paper is this: for any fixed ε> 0, 0 < α ≤ 1, and d ≥ 2 there is a distributed algorithm run-ning in O(log n·log ∗ n) communication rounds on an n-node, d-dimensional α-UBG G that computes a (1+ε)-spanner G′ of G with maximum degree Δ(G′) = O(1) and total weight w(G′) = O(w(MST (G)). This result is motivated by the topology control problem in wireless ad-hoc networks and improves on existing topology control algorithms along sev-eral dimensions. The technical contributions of the paper include a new, sequential, greedy algorithm with relaxed edge ordering and lazy updating, and clustering techniques for filtering out unnecessary edges.