Although the lift-and-project operators of Lovász and Schrijver have been the subject of intense study, their M(K , K ) operator has received little attention. We consider an application of this operator to the stable set problem. We begin with an initial linear programming (LP) relaxation consisting of clique and non-negativity inequalities, and then apply the operator to obtain a stronger ext...

In the Tree Augmentation problem we are given a tree T = (V, F ) and an additional set E ⊆ V × V of edges, called “links”, with positive integer costs {ce : e ∈ E}. The goal is to augment T by a minimum cost set of links J ⊆ E such that T ∪ J is 2-edge-connected. Let M denote the maximum cost of a link. Recently, Adjiashvili [1] introduced a novel LP for the problem and used it to break the nat...

In the current article, MHD flow problem of Darcy-Forchheimer nanoliquid comprising motile microorganisms with viscous dissipation impact past a nonlinear elongated sheet is addressed. The inclusion gyrotactic in assists to boost up thermal efficiency numerous micro-biological systems. Iterative solution single-phase attained by utilizing procedure SOR (Successive over Relaxation). influences l...

The successive overrelaxation (SOR) method is an example of a classical iterative method for the approximate solution of a system of linear equations. Its iteration matrix depends on a relaxation parameter. There is no explicit formula for the optimal relaxation parameter in terms of properties of the system matrix of a general system matrix. However, for the classical model problem of a finite...

In this report, the distribution and deviation of electric field in the active medium of the TE CO2 laser has been investigated due to the injection of net electron charge beam as a plasma generator. Some parameters of system have been considered, such as density and mean-free-path of injected charge beam. The electric potential and electric field distribution have been simulated by solving the...

We consider the k-balanced partitioning problem, where the goal is to partition the vertices of an input graph G into k equally sized components, while minimizing the total weight of the edges connecting different components. We allow k to be part of the input and denote the cardinality of the vertex set by n. This problem is a natural and important generalization of well-known graph partitioni...

We study some linear programming relaxations for the Unsplittable Flow problem on trees (UFPtree). Inspired by results obtained by Chekuri, Ene, and Korula for Unsplittable Flow on paths (UFP-path), we present a relaxation with polynomially many constraints that has an integrality gap bound of O(logn ·min{logm, logn}) where n denotes the number of tasks and m denotes the number of edges in the ...

In this paper we describe a novel generalized SOR algorithm for accelerating the convergence of the dynamic iteration method known as waveform relaxation. A new convolution SOR algorithm is presented, along with a theorem for determining the optimal convolution SOR parameter. Both analytic and experimental results are given to demonstrate that the convergence of the convolution SOR algorithm is...

We study the complete set packing problem (CSPP) where the family of feasible subsets may include all possible combinations of objects. This setting arises in applications such as combinatorial auctions (for selecting optimal bids) and cooperative game theory (for finding optimal coalition structures). Although the set packing problem has been well-studied in the literature, where exact and app...