We present a new and simpler method to implement in constant amortized time the ip operation of the so-called 'Greedy Flip Algorithm', an optimal algorithm to compute the visibility graph/complex of a collection of pairwise disjoint bounded convex sets of constant complexity. The method uses only the incidence structure of the visibility complex and only the primitive predicate which states tha...

We consider the sum-of-squares hierarchy of approximations for problem minimizing a polynomial f over boolean hypercube $${{\mathbb {B}}^{n}=\{0,1\}^n}$$ . This provides each integer $$r \in {\mathbb {N}}$$ lower bound $$\smash {f_{({r})}}$$ on minimum $$f_{\min }$$ f, given by largest scalar $$\lambda $$ which $$f - \lambda is $${\mathbb {B}}^{n}$$ with degree at most 2r. analyze quality these...

This paper deals with the Sum-Of-Sinusoids (SOS)-based simulation method for generating timecorrelated Rayleigh fading processes. Five of the most accepted and recently proposed SOS-based Rayleigh fading models have been analyzed and compared. We have used the mean and the maximum power margin quality measures to assess the accuracy of the autocorrelation function (ACF) of the generated process...

This paper addresses the problem of establishing robust asymptotical stability of discrete-time linear systems polynomially affected by time-varying uncertainty confined into a polytope. A linear matrix inequality (LMI) condition for establishing robust asymptotical stability is proposed by introducing a novel approach for establishing the existence of a common homogeneous polynomial Lyapunov f...

This paper studies the so-called bi-quadratic optimization over unit spheres min x∈Rn,y∈Rm ∑ 1≤i,k≤n, 1≤j,l≤m bijklxiyjxkyl subject to ‖x‖ = 1, ‖y‖ = 1. We show that this problem is NP-hard and there is no polynomial time algorithm returning a positive relative approximation bound. After that, we present various approximation methods based on semidefinite programming (SDP) relaxations. Our theo...