Abstract
LetV be a set inR n consisting of finitely many hyperplanes. The linear recognition problem given byV is to determine, using ternary comparisons of the form “f(x):0” wheref:R n →R is a linear function, whether a pointxεR n is inV. We consider lower bounds on the number of comparisons whenV corresponds to some NP-complete problems. A technique is proposed for proving such bounds. If the tests “f(x):0” are restricted so thatf always defines some hyperplane inV, then some NP-complete problems are shown to have exponential lower bounds inn. Examples of larger classes of linear test functions are found such that the exponential lower bounds are still valid.
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This work was supported by the Academy of Finland and by the Finnish Cultural Foundation. Partial support was provided by the National Science Foundation Grant MCS 79-15763 (Univ. of California).
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Ukkonen, E. Exponential lower bounds for some NP-complete problems in a restricted linear decision tree model. BIT 23, 181–192 (1983). https://doi.org/10.1007/BF02218439
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DOI: https://doi.org/10.1007/BF02218439