A squared-euclidean distance location-allocation problem

The limits of squared Euclidean distance regularization

Some of the simplest loss functions considered in Machine Learning are the square loss, the logistic loss and the hinge loss. The most common family of algorithms, including Gradient Descent (GD) with and without Weight Decay, always predict with a linear combination of the past instances. We give a random construction for sets of examples where the target linear weight vector is trivial to lea...

Global Optimization Approach for the Capacitated Euclidean Location-Allocation Problem

In this chapter, we present a procedure that seeks the global minimum for the capacitated Euclidean location-allocation problem which is defined as follows. Given the fixed location of m existing facilities or customers on a continuous plane and their associated demands, we wish to determine the location of n new facilities or sources with known capacities, and the allocation of its supply, in ...

Squared Metric Facility Location Problem

Jain et al. proposed two well-known algorithms for the Metric Facility Location Problem (MFLP), that achieve approximation ratios of 1.861 and 1.61. Mahdian et al. combined the latter algorithm with scaling and greedy augmentation techniques, obtaining a 1.52-approximation for the MFLP. We consider a generalization of the Squared Euclidean Facility Location Problem, when the distance function i...

A PTAS For The k-Consensus Structures Problem Under Squared Euclidean Distance

In this paper we consider a basic clustering problem that has uses in bioinformatics. A structural fragment is a sequence of ` points in a 3D space, where ` is a fixed natural number. Two structural fragments f1 and f2 are equivalent if and only if f1 = f2 · R + τ under some rotation R and translation τ . We consider the distance between two structural fragments to be the sum of the squared Euc...

Algorithmic Approaches for Solving the Euclidean Distance Location and Location-Allocation Problems