Identifying codes and searching with balls in graphs

Given a graph \(G\) and a positive integer \(R\) we address the following combinatorial search theoretic problem: What is the minimum number of queries of the form "does an unknown vertex \(v \in V(G)\) belong to the ball of radius \(r\) around \(u\)?" with \(u \in V(G)\) and \(r\le R\) th...

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Bibliographic Details
Published inarXiv.org
Main Authors Kim, Younjin, Kumbhat, Mohit, Zoltan Lorant Nagy, Patkos, Balazs, Pokrovskiy, Alexey, Mate Vizer
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 02.06.2014
Subjects
Combinatorial analysis
Graphs
Hypercubes
Queries
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Summary:Given a graph \(G\) and a positive integer \(R\) we address the following combinatorial search theoretic problem: What is the minimum number of queries of the form "does an unknown vertex \(v \in V(G)\) belong to the ball of radius \(r\) around \(u\)?" with \(u \in V(G)\) and \(r\le R\) that is needed to determine \(v\). We consider both the adaptive case when the \(j\)th query might depend on the answers to the previous queries and the non-adaptive case when all queries must be made at once. We obtain bounds on the minimum number of queries for hypercubes, the Erd\H os-Rényi random graphs and graphs of bounded maximum degree .
ISSN:2331-8422