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Identifying codes and searching with balls in graphs

Authors
  • Kim, Younjin
  • Kumbhat, Mohit
  • Nagy, Zoltan Lorant
  • Patkos, Balazs
  • Pokrovskiy, Alexey
  • Vizer, Mate
Type
Preprint
Publication Date
Jun 02, 2014
Submission Date
May 29, 2014
Identifiers
arXiv ID: 1405.7508
Source
arXiv
License
Yellow
External links

Abstract

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-R\'enyi random graphs and graphs of bounded maximum degree .

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