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An NP-Completeness Result of Edge Search in Graphs

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Abstract

Consider the following generalization of the classical sequential group testing problem for two defective items: suppose a graph G contains n vertices two of which are defective and adjacent. Find the defective vertices by testing whether a subset of vertices of cardinality at most p contains at least one defective vertex or not. What is then the minimum number c p (G) of tests, which are needed in the worst case to find all defective vertices? In Gerzen (Discrete Math 309(20):5932–5942, 2009), this problem was partly solved by deriving lower and sharp upper bounds for c p (G). In the present paper we show that the computation of c p (G) is an NP-complete problem. In addition, we establish some results on c p (G) for random graphs.

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Authors and Affiliations

  1. Institute of Communications and Navigation, German Aerospace Center (DLR), 17235, Neustrelitz, Germany

    Tatjana Gerzen

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  1. Tatjana Gerzen
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Correspondence to Tatjana Gerzen.

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Gerzen, T. An NP-Completeness Result of Edge Search in Graphs. Graphs and Combinatorics 30, 661–669 (2014). https://doi.org/10.1007/s00373-013-1287-y

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  • DOI: https://doi.org/10.1007/s00373-013-1287-y

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