On the Optimality of Network Topology Discovery in Single-Hop Bounded-Interference Networks

TL;DR

PRISM is a deterministic, efficient topology-discovery algorithm for single-hop wireless networks with bounded interference, achieving near-optimal rounds with high probability.

Contribution

It introduces PRISM, a novel scheduling framework using finite-field labels and modular arithmetic for guaranteed topology discovery.

Findings

Achieves full discovery in expected O(L(1+δ) log K) rounds

Deterministically completes in O(L^2 log K) rounds

Simulation results show near-linear scaling with interference bound L

Abstract

We propose \emph{PRISM} (\textbf{Pseudorandom Residue-based Indexed Scheduling Method}), a deterministic topology-discovery framework for single-hop wireless networks with bounded interference. Each receiver has at most \(L\) interfering transmitters among \(K\) transmitters and identifies them through singleton transmissions. PRISM assigns finite-field labels to transmitters and schedules transmissions via modular multiplication and a second prime modulus. It achieves full discovery in \(O(L(1+\delta)\log K)\) rounds in expectation with failure probability \(K^{-\delta}\), and in \(O(L^2\log K)\) rounds deterministically. Simulations show \(\approx 0.9L\log K\) scaling, with \(q/L\approx1.2\) minimizing mean completion time and \(q/L\approx1.4\text{--}1.6\) improving tail performance.