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

2026-04-21

AI Summary

This work addresses the topology discovery problem in single-hop wireless networks under bounded interference, where each receiver must identify at most $L$ interfering transmitters. The authors propose PRISM, a novel framework that introduces a pseudorandom residue-indexed scheduling mechanism, integrating finite-field labeling, modular multiplication, and dual-prime modulus scheduling to achieve deterministic topology discovery. Theoretical analysis shows that the expected number of rounds is $O(L(1+\delta)\log K)$ with failure probability at most $K^{-\delta}$, while the deterministic bound is $O(L^2 \log K)$. Simulations demonstrate that in practice only about $0.9L\log K$ rounds are needed. Moreover, the average completion time is minimized when $q/L \approx 1.2$, whereas tail performance improves for $q/L$ in the range $1.4$–$1.6$, highlighting the critical role of the $q/L$ ratio in tuning system performance.

Technology Category

• Planning, Routing, and Scheduling: Scheduling under Uncertainty
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Security and Privacy: Large-scale security measurements
• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization

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 \(O(L(1+δ)\log K)\) rounds in expectation with failure probability \(K^{-δ}\), 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.

Problem

• topology discovery
• single-hop networks
• bounded interference
• wireless networks
• interference identification

Innovation

• PRISM
• topology discovery
• bounded-interference networks
• deterministic scheduling
• finite-field labeling