The maximum value problem and NP real numbers

The maximum edge biclique problem is NP-complete

We prove that the maximum edge biclique problem in bipartite graphs is NP-complete. A biclique in a bipartite graph is a vertex induced subgraph which is complete. The problem of finding a biclique with a maximum number of vertices is known to be solvable in polynomial time but the complexity of finding a biclique with a maximum number of edges was still undecided.

The real nonnegative inverse eigenvalue problem is NP-hard

A list of complex numbers is realizable if it is the spectrum of a nonnegative matrix. In 1949 Sulěımanova posed the nonnegative inverse eigenvalue problem (NIEP): the problem of determining which lists of complex numbers are realizable. The version for reals of the NIEP (RNIEP) asks for realizable lists of real numbers. In the literature there are many sufficient conditions or criteria for lis...

On the P-NP problem over real matrix rings

The Real Dimension Problem Is Np R -complete Ecole Normale Supérieure De Lyon the Real Dimension Problem Is Np R -complete R Esum E the Real Dimension Problem Is Np R -complete

We show that computing the dimension of a semi-algebraic set of R n is a NP R-complete problem in the Blum-Shub-Smale model of computation over the reals. Since this problem is easily seen to be NP R-hard, the main ingredient of the proof is a NP R algorithm for computing the dimension. On montre que le calcul de la dimension d'un ensemble semi-alg ebrique de R n est un probl eme NP R-complet d...

Real Options Value by Monte Carlo Simulation and Fuzzy Numbers

This work presents the development of a methodology based on Monte Carlo Simulation, Fuzzy Numbers and in the Real Options Theory to determine the real options value under technical and market uncertainties. The objective of the proposed methodology is to substantially reduce the computational time involved, facilitating the decision taking process. The methodology involves: fuzzy numbers, to r...