A PTAS for the Minimum Consensus Clustering Problem with a Fixed Number of Clusters

TL;DR

This paper introduces a polynomial time approximation scheme for the Minimum Consensus Clustering problem with a fixed number of clusters, addressing its computational hardness and providing practical approximation methods.

Contribution

It presents the first PTAS for the problem with a fixed number of clusters, despite the problem being NP-hard.

Findings

PTAS exists for fixed number of clusters

NP-hardness of the restricted problem

Approximation algorithms for consensus clustering

Abstract

The Consensus Clustering problem has been introduced as an effective way to analyze the results of different microarray experiments. The problem consists of looking for a partition that best summarizes a set of input partitions (each corresponding to a different microarray experiment) under a simple and intuitive cost function. The problem admits polynomial time algorithms on two input partitions, but is APX-hard on three input partitions. We investigate the restriction of Consensus Clustering when the output partition is required to contain at most k sets, giving a polynomial time approximation scheme (PTAS) while proving the NP-hardness of this restriction.