Identifying codes and searching with balls in graphs

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 ∈ V ( G ) belong to the ball of radius r around u ?” with u ∈ V ( G ) and r ≤ 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 Erdős–Renyi random graphs and graphs of bounded maximum degree.

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