Minimum bisection is NP-hard on unit disk graphs
نویسندگان
چکیده
منابع مشابه
Minimum Bisection Is NP-hard on Unit Disk Graphs
In this paper we prove that the Min-Bisection problem is NP-hard on unit disk graphs, thus solving a longstanding open question.
متن کاملFurther Information on Publisher's Website: Httpxggdxfdoiforggihfihhugwuveqettperrrtsev 2 2 Use Policy Minimum Bisection Is Np-hard on Unit Disk Graphs
In this paper we prove that the Min-Bisection problem is NP-hard on unit disk graphs, thus solving a longstanding open question.
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We prove that the max-cut and max-bisection problems are NP-hard on unit disk graphs. We also show that λ-precision graphs are planar for λ > 1/ √ 2 and give a dichotomy theorem for max-cut computational complexity on λ-precision unit disk graphs.
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Unit disk graphs are the intersection graphs of unit diameter closed disks in the plane. This paper reduces SATISFIABILITY to the problem of recognizing unit disk graphs. Equivalently, it shows that determining if a graph has sphericity 2 or less, even if the graph is planar or is known to have sphericity at most 3, is NP-hard. We show how this reduction can be extended to 3 dimensions, thereby...
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ژورنال
عنوان ژورنال: Information and Computation
سال: 2017
ISSN: 0890-5401
DOI: 10.1016/j.ic.2017.04.010