Topology Control with Limited Geometric Information

Abstract

Abstract. Topology control is the problem of selecting neighbors for each node in a wireless network, so that the resulting network has a number of useful properties. More precisely, a topology control protocol P takes as input a network G and aims to construct a spanning subgraph GP , that is sparse, "energy minimizing" and has sufficient connectivity so as to guarantee multiple short paths between pairs of nodes in G. Currently, topology control protocols assume that nodes in G reside in some Euclidean (usually, 2-dimensional) space and rely on geometric information such as node locations and pairwise distances between nodes to produce GP with appropriate properties. However, these protocols are extremely sensitive to errors in location information and this feature makes them impractical because errors in location and distance information are pervasive in practical systems. This paper presents and analyzes two randomized topology control protocols that are tolerant to errors in pairwise distance estimates. The first protocol, called RTC (short for randomized topology control) uses no geometric information, relying only on connectivity information and is therefore completely immune to errors in location or distance information. The second protocol, called ε-RTC, generalizes the first protocol. Allowing for errors in distance estimates, but assuming that relative errors are bounded above by ε, the second protocol produces an output network that is symmetric, connected, sparse, and has good spanner properties. As ε → 0, ε-RTC behaves like the XTC protocol (R. Wattenhofer and A. Zollinger, "XTC: A practical topology control algorithm for ad-hoc networks", WMAN 2004) and for large values of ε, it behaves like RTC. Our results hold whenever the input network is a unit disk graph or even a quasi unit disk graph.

kTC - Robust and Adaptive Wireless Ad-Hoc Topology Control

“…In [14] it is shown, that small errors in the weights of XTC may lead to partitioning of the topology. Furthermore XTC's resulting topology may have high degree.…”

“…Most describe geometrical structures that can be roughly categorized into using location [11]- [13], [17], [20] or angle-of-arrival [22], [24] or being location-free using, e.g., link properties as edge weights [14], [23].…”

“…It generally meets the main requirements under favorable conditions. However, XTC is not robust in the situation of local inconsistencies: even slightly diverging measurements at neighboring nodes may lead to damage or even partition of its topology [14]. RTC and ε-RTC [14] have introduced randomness to this end.…”

“…However, XTC is not robust in the situation of local inconsistencies: even slightly diverging measurements at neighboring nodes may lead to damage or even partition of its topology [14]. RTC and ε-RTC [14] have introduced randomness to this end. However, both approaches require precise ex-ante knowledge about transmission errors or are bound to suffer from severe performance drops.…”

Topology Control Made Practical: Increasing the Performance of Source Routing

“…In [16] a generalized version of XTC called k-XTC is presented; this algorithms drops a communication link only if at least k alternative paths exist. In [17] the RTC algorithm is proposed that slightly changes XTC such that link qualities are determined randomly. In [18] the authors propose S-XTC, an extended version of [11] implemented on Bluetooth enabled sensor nodes.…”