On Okada's method for realizing cut-set matrices

Realizing symmetric set functions as hypergraph cut capacity

A set function is a function defined on a set family. It is said to be symmetric if the value for each set coincides with that for its complement. A cut capacity function of an undirected graph or hypergraph is a fundamental example of symmetric set functions, and is also submodular if the capacity on each edge or hyperedge is nonnegative. Fujishige and Patkar (2001) provided necessary and suff...

An algorithm for realizing Euclidean distance matrices

We present an efficient algorithm to find a realization of a (full) n × n squared Euclidean distance matrix in the smallest possible dimension. Most existing algorithms work in a given dimension: most of these can be transformed to an algorithm to find the minimum dimension, but gain a logarithmic factor of n in their worstcase running time. Our algorithm performs cubically in n (and linearly w...

Realizing Suleimanova-type Spectra via Permutative Matrices

On capacitated network design cut-set polyhedra

This paper provides an analysis of capacitated network design cut–set polyhedra. We give a complete linear description of the cut–set polyhedron of the single commodity – single facility capacitated network design problem. Then we extend the analysis to single commodity – multifacility and multicommodity – multifacility capacitated network design problems. Valid inequalities described here are ...

Application of cut set method to reliability evaluation of mine ventilation networks

Providing a fresh and cool airflow in underground mines is one of the main concerns during mining. Destruction of support systems, the presence of undesirable objects in the airway and distortion of airflow are the parameters involved that would result in pressure loss, which would affect the ventilation network. There are a lot of research works about the ventilation network planning that cons...