An Intersection Inequality Sharper than the Tanimoto Triangle Inequality for Efficiently Searching Large Databases

An Intersection Inequality Sharper than the Tanimoto Triangle Inequality for Efficiently Searching Large Databases

Bounds on distances or similarity measures can be useful to help search large databases efficiently. Here we consider the case of large databases of small molecules represented by molecular fingerprint vectors with the Tanimoto similarity measure. We derive a new intersection inequality which provides a bound on the Tanimoto similarity between two fingerprint vectors and show that this bound is...

On the metric triangle inequality

A non-contradictible axiomatic theory is constructed under the local reversibility of the metric triangle inequality. The obtained notion includes the metric spaces as particular cases and the generated metric topology is T$_{1}$-separated and generally, non-Hausdorff.

Triangle inequality for resistances

Given an electrical circuit each edge e of which is an isotropic conductor with a monomial conductivity function y∗ e = y r e/μ s e. In this formula, ye is the potential difference and y∗ e current in e, while μe is the resistance of e, while r and s are two strictly positive real parameters common for all edges. In 1987, Gvishiani and Gurvich [4] proved that, for every two nodes a, b of the ci...

The Poverty-Growth-Inequality Triangle

Improved estimates for the triangle inequality

We obtain refined estimates of the triangle inequality in a normed space using integrals and the Tapia semi-product. The particular case of an inner product space is discussed in more detail.