Algorithms for the preordering problem and their application to the task of jointly clustering and ordering the accounts of a social network

TL;DR

This paper introduces approximation algorithms and relaxations for the NP-hard preordering problem, applying them to jointly cluster and order social network accounts, with promising results.

Contribution

It presents a linear-time 4-approximation algorithm, tightens linear program relaxations, and applies these methods to social network account clustering and ordering.

Findings

The 4-approximation algorithm effectively constructs maximum dicuts.

Tightened linear relaxations improve bounds on the preordering problem.

Algorithms successfully applied to social network account clustering and ordering.

Abstract

The NP-hard maximum value preordering problem is both a joint relaxation and a hybrid of the clique partition problem (a clustering problem) and the partial ordering problem. Toward approximate solutions and lower bounds, we introduce a linear-time 4-approximation algorithm that constructs a maximum dicut of a subgraph and define local search heuristics. Toward upper bounds, we tighten a linear program relaxation by the class of odd closed walk inequalities that define facets, as we show, of the preorder polytope. We contribute implementations of the algorithms, apply these to the task of jointly clustering and partially ordering the accounts of published social networks, and compare the output and efficiency qualitatively and quantitatively.