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Complexity Results for Some Eigenvector Problems

By Thomas Eiter and Georg Gottlob

Abstract

We consider the computation of eigenvectors x = (x1,..., xn) over the integers, where each component xi satisfies |xi | ≤ b for an integer b. We address various problems in this context, and analyze their computational complexity. We find that different problems are complete for the complexity classes NP, P NP � , FNP//OptP[O(log n)], FPNP, P NP, and NP NP. Applying the results, finding bounded solutions of a Diophantine equation v·x T = 0 is shown to be intractable

Topics: mathematical programming, eigenvectors, problem complexity, combinatorial optimization Computing Reviews Categories, F.2.1. [Analysis of Algorithms and Problem Complexity, Numerical Algorithms and Problems – computation on matrices, G.1.6 [Numerical Analysis, Optimization – integer
Year: 2000
OAI identifier: oai:CiteSeerX.psu:10.1.1.135.6433
Provided by: CiteSeerX
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