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• W2895699666 abstract "We investigate the complexity of four decision problems dealing with the uniqueness of a solution in a graph: “Uniqueness of an r-Locating–Dominating Code with bounded size” (U-LDCr), “Uniqueness of an Optimal r-Locating–Dominating Code” (U-OLDCr), “Uniqueness of an r-Identifying Code with bounded size” (U-IdCr), “Uniqueness of an Optimal r-Identifying Code” (U-OIdCr), for any fixed integer r≥1. In particular, we describe a polynomial reduction from “Unique Satisfiability of a Boolean formula” (U-SAT) to U-OLDCr, and from U-SAT to U-OIdCr; for U-LDCr and U-IdCr, we can do even better and prove that their complexity is the same as that of U-SAT, up to polynomials. Consequently, all these problems are NP-hard, and U-LDCr and U-IdCr belong to the class DP." @default.
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• W2895699666 date "2019-05-01" @default.
• W2895699666 modified "2023-10-14" @default.
• W2895699666 title "Unique (optimal) solutions: Complexity results for identifying and locating–dominating codes" @default.
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• W2895699666 doi "https://doi.org/10.1016/j.tcs.2018.09.034" @default.
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