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arXiv · 2307.16312

Open-locating-dominating sets with error correction

Devin Jean·Suk Seo
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Abstract

An open-locating-dominating set of a graph models a detection system for a facility with a possible "intruder" or a multiprocessor network with a possible malfunctioning processor. A "sensor" or "detector" is assumed to be installed at a subset of vertices where it can detect an intruder or a malfunctioning processor in their neighborhood, but not at itself. We consider a fault-tolerant variant of an open-locating-dominating set called an error-correcting open-locating-dominating set, which can correct a false-positive or a false-negative signal from a detector. In particular, we prove the problem of finding a minimum error-correcting open-locating-dominating set in an arbitrary graph is NP-complete. Additionally, we characterize the existence criteria for an error-correcting open-locating-dominating sets for an arbitrary graph. We also consider extremal graphs that require every vertex to be a detector and minimum error-correcting open-locating-dominating sets in infinite grids.

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Devin Jean, Suk Seo. 2023-07-30. Open-locating-dominating sets with error correction. https://arxiv.org/abs/2307.16312

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