Distributed Backbone Structure for Algorithms in the SINR Model of Wireless Networks

Abstract

The Signal-to-Interference-and-Noise-Ratio (SINR) physical model is one of the legitimate models of wireless networks. Despite of the vast amount of study done in design and analysis of centralized algorithms supporting wireless communication under the SINR physical model, little is known about distributed algorithms in this model, especially deterministic ones. In this work we construct, in a deterministic distributed way, a backbone structure on the top of a given wireless network, which can be used for transforming many algorithms designed in a simpler model of ad hoc broadcast networks without interference into the SINR physical model with uniform power of stations, without increasing their asymptotic time complexity. The time cost of the backbone data structure construction is only O(∆polylogn) rounds, where ∆ is roughly the inverse of network density and n is the number of nodes in the whole network. The core of the construction is a novel combinatorial structure called SINR-selector, which is introduced and constructed in this paper. We demonstrate the power of the backbone data structure by using it for obtaining efficient O(D + ∆polylog n)-round and O(D + k + ∆polylog n)-round deterministic distributed solutions for leader election and multi-broadcast, respectively, where D is the network diameter and k is the number of messages to be disseminated. † The first condition is a straightforward application of the SINR ratio, comparing strength of one of the received signals with the remainder. The second condition enforces the signal to be sufficiently strong in order to be distinguished from the background noise, and thus to be decoded.

Fair Maximal Independent Sets

“…From a practical perspective, we note that MIS algorithms are often used as subroutines by higher-level applications [6,7,9,15,19]. It follows that joining (or not joining) the MIS might have a consequence in terms of a node's expected work.…”

“…Distributed solutions to the MIS problem provide a key symmetry-breaking function. Accordingly, these algorithm are often used as subroutines in higher-level applications, including the construction of network backbones [6,9], leader election [4], resource allocation [19], key exchange [7], and image processing [15].…”

Dynamic multiple-message broadcast

“…In the SINR model with restricted sensitivity, so called weak-sensitivity device model, Jurdzinski and Kowalski [20] designed an algorithm spanning an efficient backbone sub-network, that might be used for efficient implementation of multi-broadcast.…”

A Self-Stabilizing Algorithm for CDS Construction with Constant Approximation in Wireless Networks under SINR Model

“…Based on DSS M IS, we propose a distributed CDS algorithm with a constant approximation factor, which can terminate within O(log n). Compared with the algorithm in [14] within O(Δpoly log n), our algorithm has a O(poly log n) times improvement of time complexity. In addition, our algorithm is more robust than that of the algorithm in [14], as we also consider the self-stabilizing problem of the system during the process of CDS construction.…”

“…For dominating set construction, in 2008, Santi gave the first constant density algorithm in the SINR model with physical carrier sensing [13]. In 2012, Jurdzinski and Kowalski proposed the first CDS construction algorithm with SINR constraint [14]. In addition, self-stabilization is a theoretical framework of non-masking fault-tolerant distributed algorithms proposed by Dijkstra [15].…”