One way to study the combinatorics of finite metric spaces is betweenness relation associated with space. In hypergraph metrization problem, one has find and characterize betweennesses collinear triples (or alternatively, non-degenerate triangles) that coincide edges a given 3-uniform hypergraph. Metrizability different kinds hypergraphs was investigated in last decades. Chen showed Steiner tri...

In this paper, we consider the concepts farthest points and nearest points in normed linear spaces, We obtain a necessary and coecient conditions for proximinal, Chebyshev, remotal and uniquely remotal subsets in normed linear spaces. Also, we consider -remotality, -proximinality, coproximinality and co-remotality.

We show that the problem of finding optimal strategies for both players in a simple stochastic game reduces to the generalized linear complementarity problem (GLCP) with a P-matrix, a well-studied problem whose hardness would imply NP = co-NP. This makes the rich GLCP theory and numerous existing algorithms available for simple stochastic games. As a special case, we get a reduction from binary...

A combinatorial simplex algorithm is an instance of the simplex method in which the pivoting depends on combinatorial data only. We show that any algorithm of this kind admits a tropical analogue which can be used to solve mean payoff games. Moreover, any combinatorial simplex algorithm with a strongly polynomial complexity (the existence of such an algorithm is open) would provide in this way ...

This paper explores the use of a non-parametric frontier approach to analyse multi-factor productivity across time and countries. We argue that conventional measures of total factor productivity involve some restrictive assumptions that might bias the results. A non-parametric approach avoids these assumptions. The model uses linear programming techniques to examine the productivity catching-up...

Summary data take the form of a triple that consists of a summary attribute, a category and a numeric value. The inference problem of summary data consists in deciding whether or not a summary data of interest is evaluable (i.e., can be computed) from a given set of summary data. We address the special case of the inference problem with homogeneous summary data (i.e., summary data with the same...