A Correction to this paper has been published: 10.1007/s00022-022-00630-w

Some sharp discrete inequalities in normed linear spaces are obtained. New reverses of the generalised triangle inequality are also given.

S growth or inequality be prioritized in the design and execution of development policies? An oft cited paper by Dollar and Kraay of the World Bank advocates growth as the primary objective of development. Opponents argue that growth may not be pro-poor, thus growth alone is insufficient for poverty reduction— the ultimate goal of development. They instead emphasize redistribution as an importa...

Some sharp quadratic reverses for the generalised triangle inequality in inner product spaces and applications are given.

Refining some results of S. S. Dragomir, several new reverses of the triangle inequality in inner product spaces are obtained.

Several refinements of the Finsler-Hadwiger inequality and its reverse in the triangle are discussed. A new one parameter family of Finsler-Hadwiger inequalities and their reverses are proved. This allows us to obtain new bounds for the sum of the squares of the side lengths of a triangle in terms of other elements in the triangle. Finally, these new bounds are compared to known ones.

A new class of algorithms based on the triangle inequality has recently been proposed for use in contentbased image retrieval. These algorithms rely on comparing a set of key images to the database images, and storing the computed distances. Query images are later compared to the keys, and the triangle inequality is used to speedily compute lower bounds on the distance from the query to each of...

The k center problem with triangle inequality is that of placing k center nodes in a weighted undirected graph in which the edge weights obey the triangle inequality so that the maximum distance of any node to its nearest center is minimized In this paper we consider a generalization of this problem where given a number p we wish to place k centers so as to minimize the maximum distance of any ...

A new solution method to the Nearest Neighbour Problem is presented. The method is based upon the triangle inequality and works well for small point sets, where traditional solutions are particularly ineffective. Its performance is characterized experimentally and compared with k-d tree and Elias approaches. A hybrid approach is proposed wherein the triangle inequality method is applied to the ...

Consider a complete graph G with the edge weights satisfying the β-sharpened triangle inequality: weight(u, v) ≤ β(weight(u, x)+ weight(x, v)), for 1/2 ≤ β < 1. We study the NP-hard problem of finding a minimum weight spanning subgraph of G which is k-vertex-connected, k ≥ 2, and give a detailed analysis of an approximation quadratic-time algorithm whose performance ratio is β 1−β . The algorit...