Local approximation schemes for topology control
Proceedings of the twenty-fifth annual ACM symposium on Principles of distributed computing - PODC '06
This paper presents a distributed algorithm for wireless adhoc 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" assumption of UDGs and also
... f 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 running 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 ∆(G ) = O(1) and total weight w(G ) = O(w(M ST (G)). This result is motivated by the topology control problem in wireless ad-hoc networks and improves on existing topology control algorithms along several 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. ad-hoc wireless networks. In this paper we present a fast distributed algorithm for constructing a linear size, lightweight t-spanner of bounded degree for any given t > 1, on wireless networks. Below, we describe our result more precisely.