A simple relaxation of two rows of a simplex tableau is a mixed integer set consisting of two equations with two free integer variables and non-negative continuous variables. Recently Andersen et al. [2] and Cornu ́ejols and Margot [13] showed that the facet-defining inequalities of this set are either split cuts or intersection cuts obtained from lattice-free triangles and quadrilaterals. Throu...

A simple relaxation of two rows of a simplex tableau is a mixed integer set consisting of two equations with two free integer variables and non-negative continuous variables. Recently Andersen et al. [3] and Cornuéjols and Margot [17] showed that the facet-defining inequalities of this set are either split cuts or intersection cuts obtained from lattice-free triangles and quadrilaterals. Throug...

Round trip times (RTTs) play an important role in Internet measurements. In this paper, we explore some of the ways in which routing policies impact RTTs. In particular, we investigate how routing policies for both intraand inter-domain routing can naturally give rise to violations of the triangle inequality with respect to RTTs. Triangle Inequality Violations (TIVs) might be exploited by overl...

Some additive reverses of the generalised triangle inequality in normed linear spaces are given. Applications for complex numbers are provided as well.

The above norm induces a metric d where d(f, g) = ‖f − g‖p. Note that d(f, g) = 0 if and only if f = g a.e. μ, in which case we identify f with g. The Lp norm, like all worthy norms, satisfies the triangle inequality: ‖f + g‖p ≤ ‖f‖p + ‖g‖p ; this is precisely Minkowski’s inequality. For random variables X, Y defined on the same probability space and having finite p’th moments, Minkowski’s ineq...

In the course of realizing certain triangle centers as points that minimize certain quantities, C. Kimberling and P. Moses, in Math. Mag. 85 (2012) 221–227, discovered an inequality in three variables that generalizes the Cauchy-Schwarz inequality, and made a conjecture regarding a generalization of that inequality to an arbitrary number of variables. In this paper, we give a proof of a stronge...