The primal-dual method increases the dual variables gradually until some dual constraint becomes tight. Then, the primal variable corresponding to the tight dual constraint is ‘bought’ (or selected), and the process continues till we get a feasible primal solution. Next, we compare the value of the primal solution to the value of the dual solution to get an appropriate approximation factor (or ...

In the Petrol Station Replenishment Problem (PSRP) the aim is to jointly determine an allocation of petroleum products to tank truck compartments and to design delivery routes to stations. This article describes an exact algorithm for the PSRP. This algorithm was extensively tested on randomly generated data and on a real-life case arising in Eastern Quebec.

Given an undirected graph, the Vertex Coloring Problem (VCP) consists of assigning a color to each vertex of the graph in such a way that two adjacent vertices do not share the same color and the total number of colors is minimized. DSATUR-based Branch-and-Bound algorithm (DSATUR) is an effective exact algorithm for the VCP. One of its main drawback is that a lower bound is computed only once a...

OBJECTIVE The purpose of our study was to assess the differentially diagnostic value of radiographic characteristics of pure ground glass nodules (GGNs) between minimally invasive adenocarcinoma and non-invasive neoplasm. METHODS Sixty-seven pure GGNs (28 minimally invasive adenocarcinomas (MIA) and 39 pre-invasive lesions) were analyzed from June 2012 to June 2015. Pre-invasive lesions consi...

A large class of new exact solutions to the steady, incompressible Euler equation on plane is presented. These hybrid consist a set stationary point vortices embedded in background sea Liouville-type vorticity that exponentially related stream function. The input construction "pure" vortex equilibrium irrotational flow. Pure equilibria also appear as parameter $A$ approaches limits $A\to 0,\inf...

the article presents explanation and analysis of plotinus’ abstraction theology. in this theology he tries to get negative knowledge of the god. the meaning of the negation is neither of pure negation or privation but it is based on abstraction which purifies and abstracts one concept from else to attain the exact and true meaning of it. accordingly, this method of theology is the same as the r...

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...

We consider coordination of multiple robots in a common environment, each robot having its own (distinct) roadmap. Our primary contribution is a classification of and exact algorithm for computing vector-valued — or Pareto — optima for collision-free coordination. We indicate the utility of new geometric techniques from CAT(0) geometry and give an argument that curvature bounds are the key dist...

A terrain T is an x-monotone polygonal chain in the plane; T is orthogonal if each edge of T is either horizontal or vertical. In this paper, we give an exact algorithm for the problem of guarding the convex vertices of an orthogonal terrain with the minimum number of reflex vertices.

Symmetric function theory provides a basis for computing Galois groups which is largely independent of the coefficient ring. An exact algorithm has been implemented over Q(t1, t2, . . . , tm) in Maple for degree up to 8. A table of polynomials realizing each transitive permutation group of degree 8 as a Galois group over the rationals is included.