We study a general class of non-cooperative games coming from combinatorial covering and facility location problems. A game for k players is based on an integer programming formulation. Each player wants to satisfy a subset of the constraints. Variables represent resources, which are available in costly integer units and must be bought. The cost can be shared arbitrarily between players. Once a...

This paper presents a new method for determining efficient spatial distributions of police patrol areas. This method employs a traditional maximal covering formulation and an innovative backup covering formulation to provide alternative optimal solutions to police decision makers, and to address the lack of objective quantitative methods for police area design in the literature or in practice. ...

in this paper, we develop a capacitated location-covering model considering interval values for demand and service parameters. we also consider flexibility on distance standard for covering demand nodes by the servers. we use the satisfaction degree to represent the constraint of service capacity. the proposed model belongs to the class of mixed integer programming models. our model can be redu...

We point out that there are compact 4-manifolds which do not admit metrics of positive scalar curvature, but nonetheless have finite covering spaces which do carry such metrics. Moreover, passing from a 4-manifold to a covering space sometimes actually changes the sign of the Yamabe invariant. As was first pointed out by Bérard Bergery [1], there exist, in dimensions ≡ 1 or 2 mod 8, n ≥ 9, cert...

In this article we focus on constructing an algorithm that automatizes the generation of LPN solving algorithms from the considered parameters. When searching for an algorithm to solve an LPN instance, we make use of the existing techniques and optimize their use. We formalize an LPN algorithm as a path in a graph G and our algorithm is searching for the optimal paths in this graph. The results...

Spaces with radially symmetric curvature at base point p are shown to be diffeomorphic to space forms. Furthermore, they are either isometric to Rn or Sn under a radially symmetric metric, to RPn with Riemannian universal covering of Sn equipped with a radially symmetric metric, or else have constant curvature outside a metric ball of radius equal to the injectivity

If g(t) is a three-dimensional Ricci flow solution, with sectional curvatures that are O(t) and diameter that is O(t 1 2 ), then the pullback Ricci flow solution on the universal cover approaches a homogeneous expanding soliton.