Let V be a finite configuration of voter ideal points in the Euclidean plane. For given > 0 a point x ∈ < is in the -core if for all y 6= x, ||v−x|| ≤ ||v− y||+ for a simple majority (at least |V |/2) of voters v ∈ V . Let (x) denote the the least for which x is in the -core. Thus (x) = 0 if and only if x is a core point. The least for which the -core is nonempty is denoted ∗. This paper provid...

This paper addresses the computation of the frequency response gain of sampled-data systems with their intersample behavior taken into account. The proposed method is based upon a novel necessary and sufficient condition for the frequency-response gain to be less than a given γ > 0 and thus can be used as a basis for a bisection algorithm. Unlike all currently existing results, the proposed pro...

Given an undirected graph G = (V,E), we consider the graph bisection problem, which consists in partitioning the nodes of G in two disjoined sets with p and n− p nodes respectively such that the total weight of edges crossing between subsets is minimal. We apply QCR to it, a general method, presented in [4], which combines semidefinite programming (SDP) and Mixed Integer Quadratic Programming (...

While semidefinite relaxations are known to deliver good approximations for combinatorial optimization problems like graph bisection, their practical scope is mostly associated with small dense instances. For large sparse instances, cutting plane techniques are considered the method of choice. These are also applicable for semidefinite relaxations via the spectral bundle method, which allows to...

Abstract. Community detection is a fundamental problem in the domain of complexnetwork analysis. It has received great attention, and many community detection methods have been proposed in the last decade. In this paper, we propose a divisive spectral method for identifying community structures from networks, which utilizes a sparsification operation to pre-process the networks first, and then ...

We define a weak compatibility condition for the Newest Vertex Bisection algorithm on simplex grids of any dimension and show that using this condition the iterative algorithm terminates successfully. Additionally we provide an O(n) algorithm that renumbers any simplex grid to fulfil this condition. Furthermore we conduct experiments to estimate the distance to the standard compatibility and al...

4 Some specific cutting-plane methods 12 4.1 Bisection method on R . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 4.2 Center of gravity method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 4.3 MVE cutting-plane method . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 4.4 Chebyshev center cutting-plane method . . . . . . . . . . . . . . . . . . . . . 16 4.5 ...

linear state bisection is introduced as a new method to find time-invariant state feedback control laws for a special form of underactuated nonlinear systems. the specialty of the systems considered is that every unactuated state should be coupled with at least two directly actuated states. the basic idea is based on bisecting actuated states and using linear combinations with adjustable parame...

In this paper,we treat fuzzy linear programming problemswith uncertain parameterswhose ranges are specified as fuzzy polytopes. The problem is formulated as a necessity measure optimization model. It is shown that the problem can be reduced to a semi-infinite programming problem and solved by a combination of a bisection method and a relaxation procedure. An algorithm in which the bisection met...

The embarrassingly parallel nature of the Bisection Algorithm makes it easy and efficient to program on a computer, but with an expensive time cost when all symmetric tridiagonal eigenvalues are wanted. In addition, few methods can calculate single eigenvalue in for now, especially specific order. This paper solves issue new approach that parallelize iteration. Some pseudocodes numerical result...