# Subgraph Detection with cues using Belief Propagation

1 MAESTRO - Models for the performance analysis and the control of networks
CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : We consider an Erdos-Renyi graph with $n$ nodes and edge probability $q$ that is embedded with a random subgraph of size $K$ with edge probabilities $p$ such that $p>q.$ We address the problem of detecting the subgraph nodes when only the graph edges are observed, along with some extra knowledge of a small fraction of subgraph nodes, called cued vertices or cues. We employ a local and distributed algorithm called belief propagation (BP). Recent works on subgraph detection without cues have shown that global maximum likelihood (ML) detection strictly outperforms BP in terms of asymptotic error rate, namely, there is a threshold condition that the subgraph parameters should satisfy below which BP fails in achieving asymptotically zero error, but ML succeeds. In contrast, we show that when the fraction of cues is strictly bounded away from zero, i.e., when there exists non-trivial side-information, BP achieves zero asymptotic error even below this threshold, thus approaching the performance of ML detection.
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https://hal.inria.fr/hal-01394889
Submitted on : Thursday, November 10, 2016 - 11:09:06 AM
Last modification on : Tuesday, January 9, 2018 - 10:50:02 AM
Document(s) archivé(s) le : Wednesday, March 15, 2017 - 3:49:26 AM

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### Identifiers

• HAL Id : hal-01394889, version 1
• ARXIV : 1611.04847

### Citation

Arun Kadavankandy, Konstantin Avrachenkov, Laura Cottatellucci, Sundaresan Rajesh. Subgraph Detection with cues using Belief Propagation. [Research Report] Inria Sophia Antipolis. 2016. ⟨hal-01394889v1⟩

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