Similar Elements and Metric Labeling on Complete Graphs

TL;DR

This paper introduces efficient approximation algorithms for the similar elements problem and metric labeling on complete graphs, providing solutions within a factor of 2 of the optimal, with applications in machine learning.

Contribution

It presents the first efficient 2-approximation algorithms for both the similar elements problem and metric labeling on complete graphs, advancing optimization techniques in this area.

Findings

Provides a 2-approximation algorithm for the similar elements problem.

Develops a 2-approximation algorithm for metric labeling on complete graphs.

Demonstrates applications in machine learning and pattern recognition.

Abstract

We consider a problem that involves finding similar elements in a collection of sets. The problem is motivated by applications in machine learning and pattern recognition. We formulate the similar elements problem as an optimization and give an efficient approximation algorithm that finds a solution within a factor of 2 of the optimal. The similar elements problem is a special case of the metric labeling problem and we also give an efficient 2-approximation algorithm for the metric labeling problem on complete graphs.