Broadcasting in Networks of Unknown Topology in the Presence of Swamping

TL;DR

This paper introduces efficient broadcasting algorithms for wireless networks under the novel swamping communication model, providing optimal time complexities for lattice and unknown topology networks in one and two dimensions.

Contribution

It proposes new algorithms for broadcasting in swamping networks with unknown topology, achieving optimal time complexities in various network geometries.

Findings

Optimal broadcasting algorithms for lattice networks in 1D and 2D.

Broadcast algorithms for unknown topology networks with specific time bounds.

Analysis of time complexity based on network parameters and geometry.

Abstract

In this paper, we address the problem of broadcasting in a wireless network under a novel communication model: the {\em swamping} communication model. In this model, nodes communicate only with those nodes at geometric distance greater than $s$ and at most $r$ from them. Communication between nearby nodes under this model can be very time consuming, as the length of the path between two nodes within distance $s$ is only bounded above by the diameter $D$, in many cases. For the $n$-node lattice networks, we present algorithms of optimal time complexity, respectively $O(n/r + r/(r-s))$ for the lattice line and $O(\sqrt{n}/r + r/(r-s))$ for the two-dimensional lattice. We also consider networks of unknown topology of diameter $D$ and of a parameter $g$ ({\em granularity}). More specifically, we consider networks with $\gamma$ the minimum distance between any two nodes and $g = 1/\gamma$. We present broadcast algorithms for networks of nodes placed on the line and on the plane with respective time complexities $O(D/l + g^2)$ and $O(Dg/l + g^4)$, where $l \in \Theta(\max\{(1-s),\gamma\})$.