In this note, we consider the permutahedron, the convex hull of all permutations of {1, 2 · · · , n}. We show how to obtain an extended formulation for this polytope from any sorting network. By using the optimal Ajtai-Komlós-Szemerédi (AKS) sorting network, this extended formulation has Θ(n log n) variables and inequalities. Furthermore, from basic polyhedral arguments, we show that this is be...

We study the problem of computing an equitable 2-fan for three masses distributed on the 2-sphere. The existence of an equitable 2-fan was shown by Bárány and Matoušek [3]. The contribution of this paper is two-fold. (i) We prove the existence of an infinite set of equitable 2-fans. (ii) We present an efficient algorithm for finding an equitable 2fan when the mass distributions are discrete, i....

background: bombesin shows high affinity for gastrin-releasing peptide (grp) receptors which over expressed on the cell surfaces of several human tumors particularly in prostate and breast cancers. the aim of this study was labeling of designed analogue with99mtc via hynic and tricine /edda and evaluation as potential targeted tumor scintigraphic agent.materials and methods: hynic-bombesin was ...

An equitable k-coloring of a graph is defined by a partition of its vertices into k disjoint stable subsets, such that the difference between the cardinalities of any two subsets is at most one. The equitable coloring problem consists of finding the minimum value of k such that a given graph can be equitably k-colored. We present two new integer programming formulations based on representatives...

Maritime delimitation usually starts with the calculation of an equidistance line, which is often corrected for special circumstances. The correction process aims to produce a line that is “equitable”, a concept open to various interpretations. While the equidistance line is calculated by a technical expert, an equitable line is the result of a negotiation process. Technical support is, in that...

A subset D of V (G) is called an equitable dominating set of a graph G if for every v ∈ (V − D), there exists a vertex u ∈ D such that uv ∈ E(G) and |deg(u) − deg(v)| 6 1. The minimum cardinality of such a dominating set is denoted by γe(G) and is called equitable domination number of G. In this paper we introduce the equitable edge domination and equitable edge domatic number in a graph, exact...