Given a random graph G = G n;1=2 , we give almost sure bounds for the value of the minimum bisection of G. The lower bound is obtained by applying the rst moment method, while the upper bound is given by the analysis of a simple algorithm. Moreover, these results enable us to derive upper bounds for the maximum bisection and the maxcut of G.

Abstract A bisection of a graph G is partition its vertex set into two parts the same cardinality. k -bisection such that every component each part has at most vertices. Cui and Liu proved claw-free cubic contains 2-bisection. In this paper, we improve result showing 2-bisection with bounded number monochromatic edges, where edge an connecting vertices We also prove our bound best possible for ...

We discuss algorithms for graph bisection which are relevant to the distribution of tasks, such as the elements and nodes of an unstructured mesh to the processors of a parallel computer. Starting with a cost function consisting of a part to ensure equal numbers of tasks for each processor, and a part to minimize communication time between processors, we derive the spectral bisection method, wh...

Recently several robust control designs have been proposed to the load-frequency control (LFC) problem. However, the importance and difficulties in the selection of weighting functions of these approaches and the pole-zero cancellation phenomenon associated with it produces closed loop poles. Also the order of robust controllers is as high as the plant. This gives rise to complex structure of s...

The problem of graph partitioning is of major importance for a broad range of applications. VLSI-Layout and parallel programming are only two examples where large graphs have to be cut into pieces. The partitioning of a graph into several clusters is often done by recursive bisection. Bisection heuristics are usually divided into global and local methods. Popular global methods are inertial or ...

A bisection of a graph with n vertices is a partition of its vertices into two sets, each of size n=2. The bisection size is the number of edges connecting the two sets. Finding the bisection of minimum size is NP-hard. We present an algorithm that nds a bisection that is within O(p n log n) of optimal. No sublinear approximation ratio for bisection was previously known.

Abstract The aim of the current work is to generalize well-known bisection method using quantum calculus approach. results for different values parameter q are analyzed, and rate convergence each $q\in (0,1)$ q ∈ ( 0 , 1 )</mml:m...

Using the bisection as well as the Newton-Raphson method, we compute to high precision the Littlewood-Salem-Izumi constant frequently occurring in the theory of trigonometric sums.

We develop and analyze a bisection type global optimization algorithm for real Lipschitz functions. The suggested method combines the branch and bound method with an always convergent solver of nonlinear equations. The computer implementation and performance are investigated in detail.

in this paper, we study the problem of minimizing the ratio of two quadratic functions subject to a quadratic constraint. first we introduce a parametric equivalent of the problem. then a bisection and a generalized newton-based method algorithms are presented to solve it. in order to solve the quadratically constrained quadratic minimization problem within both algorithms, a semidefinite optim...