Local Approximation Schemes for Topology Control

TL;DR

This paper introduces a distributed algorithm for wireless networks that efficiently constructs lightweight, low-degree spanners in higher-dimensional models considering real-world signal issues, improving topology control methods.

Contribution

It presents a novel distributed algorithm for constructing (1+ε)-spanners in d-dimensional α-UBGs with optimal properties, advancing topology control in realistic wireless network models.

Findings

Runs in O(log n log* n) rounds for n-node networks

Constructs spanners with O(1) maximum degree

Achieves total weight within O(1) of the MST

Abstract

This paper presents a distributed algorithm on wireless ad-hoc networks that runs in polylogarithmic number of rounds in the size of the network and constructs a linear size, lightweight, (1+\epsilon)-spanner for any given \epsilon > 0. A wireless network is modeled by a d-dimensional \alpha-quasi unit ball graph (\alpha-UBG), which is a higher dimensional generalization of the standard unit disk graph (UDG) model. The d-dimensional \alpha-UBG model goes beyond the unrealistic ``flat world'' assumption 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 \epsilon > 0, 0 < \alpha \le 1, and d \ge 2, there is a distributed algorithm running in O(\log n \log^* n) communication rounds on an n-node, d-dimensional \alpha-UBG G that computes a (1+\epsilon)-spanner G' of G with maximum degree \Delta(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 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.