On the Distributed Computation of Fractional Connected Dominating Set Packings

TL;DR

This paper presents a new distributed algorithm for computing fractional connected dominating set packings in wireless networks, improving throughput by explicitly establishing connections among tentative dominating sets.

Contribution

The paper introduces a modified distributed algorithm that enhances previous methods for computing FCDS packings under specific network conditions, explicitly connecting tentative dominating sets.

Findings

Achieves near-optimal throughput of Θ(k/ log n) messages.

Improves upon previous algorithms for certain network parameters.

Explicitly computes connections between tentative dominating sets.

Abstract

One of the most fundamental problems in wireless networks is to achieve high throughput. Fractional Connected Dominating Set (FCDS) Packings can achieve a throughput of ${\Theta}(k/\log n)$ messages for networks with node connectivity $k$, which is optimal regarding routing-based message transmission. FCDS were proposed by Censor-Hillel \emph{et al.} [SODA'14,PODC'14] and are a natural generalization to Connected Dominating Sets (CDS), allowing each node to participate with a fraction of its weight in multiple FCDS. Thus, $\Omega(k)$ co-existing transmission backbones are established, taking full advantage of the networks connectivity. We propose a modified distributed algorithm that improves upon previous algorithms for $k\Delta \in o(\min\{\frac{n \log n}{k} ,D,\sqrt{n \log n} \log^* n\}\log n)$, where $\Delta$ is the maximum node degree, $D$ the diameter and $n$ the number of nodes in the network. We achieve this by explicitly computing connections between tentative dominating sets.