TY - GEN

T1 - Detecting a Planted Bipartite Graph

AU - Rotenberg, Asaf

AU - Huleihel, Wasim

AU - Shayevitz, Ofer

N1 - Publisher Copyright:
© 2023 IEEE.

PY - 2023

Y1 - 2023

N2 - We consider the task of detecting a hidden bipartite subgraph in a given random graph. Specifically, under the null hypothesis, the graph is a realization of an Erdos-Rényi random graph over n vertices with edge density q. Under the alternative, there exists a planted kR × kL bipartite subgraph with edge density p > q. We derive asymptotically tight upper and lower bounds for this detection problem in both the dense regime, where q, p = T(1), and the sparse regime where q, p = T(n-a), a ? (0, 2]. Moreover, we consider a variant of the above problem, where one can only observe a relatively small part of the graph, by using at most Q edge queries. For this problem, we derive upper and lower bounds in both the dense and sparse regimes, and observe a gap between them.

AB - We consider the task of detecting a hidden bipartite subgraph in a given random graph. Specifically, under the null hypothesis, the graph is a realization of an Erdos-Rényi random graph over n vertices with edge density q. Under the alternative, there exists a planted kR × kL bipartite subgraph with edge density p > q. We derive asymptotically tight upper and lower bounds for this detection problem in both the dense regime, where q, p = T(1), and the sparse regime where q, p = T(n-a), a ? (0, 2]. Moreover, we consider a variant of the above problem, where one can only observe a relatively small part of the graph, by using at most Q edge queries. For this problem, we derive upper and lower bounds in both the dense and sparse regimes, and observe a gap between them.

UR - http://www.scopus.com/inward/record.url?scp=85171466588&partnerID=8YFLogxK

U2 - 10.1109/ISIT54713.2023.10206786

DO - 10.1109/ISIT54713.2023.10206786

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AN - SCOPUS:85171466588

T3 - IEEE International Symposium on Information Theory - Proceedings

SP - 1237

EP - 1242

BT - 2023 IEEE International Symposium on Information Theory, ISIT 2023

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 2023 IEEE International Symposium on Information Theory, ISIT 2023

Y2 - 25 June 2023 through 30 June 2023

ER -