Abstract:We study the complexity of the problem Detection Pair. A detection pair of a graph G is a pair (W, L) of sets of detectors with W ⊆ V (G), the watchers, and L ⊆ V (G), the listeners, such that for every pair u, v of vertices that are not dominated by a watcher of W , there is a listener of L whose distances to u and to v are different. The goal is to minimize |W | + |L|. This problem generalizes the two classic problems Dominating Set and Metric Dimension, that correspond to the restrictions L = ∅ and W = ∅, r… Show more
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