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arXiv · 2604.19978

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

Tolunay Seyfi·Erfan Khadem·Fatemeh Afghah
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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.

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Tolunay Seyfi, Erfan Khadem, Fatemeh Afghah. 2026-04-21. On the Optimality of Network Topology Discovery in Single-Hop Bounded-Interference Networks. https://arxiv.org/abs/2604.19978

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