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Identifying codes and searching with balls in graphs
- Publication Year :
- 2014
-
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 .
- Subjects :
- Mathematics - Combinatorics
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1405.7508
- Document Type :
- Working Paper