In this paper an error in[4]is pointed out and a method for constructingsurface interpolating scattered data points is presented.The main feature of the methodin this paper is that the surface so constructed is polyno...In this paper an error in[4]is pointed out and a method for constructingsurface interpolating scattered data points is presented.The main feature of the methodin this paper is that the surface so constructed is polynomial,which makes the construction simple and the calculation easy.展开更多
A weighted edge-coloured graph is a graph for which each edge is assigned both a positive weight and a discrete colour, and can be used to model transportation and computer networks in which there are multiple transpo...A weighted edge-coloured graph is a graph for which each edge is assigned both a positive weight and a discrete colour, and can be used to model transportation and computer networks in which there are multiple transportation modes. In such a graph paths are compared by their total weight in each colour, resulting in a Pareto set of minimal paths from one vertex to another. This paper will give a tight upper bound on the cardinality of a minimal set of paths for any weighted edge-coloured graph. Additionally, a bound is presented on the expected number of minimal paths in weighted edge-bicoloured graphs. These bounds indicate that despite weighted edge-coloured graphs are theoretically intractable, amenability to computation is typically found in practice.展开更多
文摘In this paper an error in[4]is pointed out and a method for constructingsurface interpolating scattered data points is presented.The main feature of the methodin this paper is that the surface so constructed is polynomial,which makes the construction simple and the calculation easy.
基金supported by Católica del Maule University Through the Project MECESUP–UCM0205
文摘A weighted edge-coloured graph is a graph for which each edge is assigned both a positive weight and a discrete colour, and can be used to model transportation and computer networks in which there are multiple transportation modes. In such a graph paths are compared by their total weight in each colour, resulting in a Pareto set of minimal paths from one vertex to another. This paper will give a tight upper bound on the cardinality of a minimal set of paths for any weighted edge-coloured graph. Additionally, a bound is presented on the expected number of minimal paths in weighted edge-bicoloured graphs. These bounds indicate that despite weighted edge-coloured graphs are theoretically intractable, amenability to computation is typically found in practice.
