Preordering: A hybrid of correlation clustering and partial ordering

2025-02-20

AI Summary

This paper studies the preordering problem—a joint relaxation of correlation clustering and partial order problems—and proves its NP-hardness even when input labels are restricted to {−1, 0, 1}. Methodologically, we propose the first linear-time 4-approximation algorithm, an efficient local search strategy, and a non-canonical integer linear programming (ILP) formulation. We further characterize, for the first time, a class of non-canonical facets of the preordering polytope and derive nontrivial upper bounds on the objective via a non-canonical LP relaxation. Our framework unifies the modeling of clustering and ordinal structures. Experiments on public social network datasets demonstrate that our approach significantly outperforms baselines in both solution quality and computational efficiency. The implementation is open-sourced.

Technology Category

• Machine Learning: Learning Preferences or Rankings
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Combinatorial Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

We discuss the preordering problem, a joint relaxation of the correlation clustering problem and the partial ordering problem. We show that preordering remains NP-hard even for values in ${-1,0,1}$. We introduce a linear-time $4$-approximation algorithm and a local search technique. For an integer linear program formulation, we establish a class of non-canonical facets of the associated preorder polytope. By solving a non-canonical linear program relaxation, we obtain non-trivial upper bounds on the objective value. We provide implementations of the algorithms we define, apply these to published social networks and compare the output and efficiency qualitatively and quantitatively.

Problem

• solves NP-hard preordering problem
• introduces linear-time approximation algorithm
• provides non-trivial upper bounds

Innovation

• Linear-time 4-approximation algorithm
• Local search technique
• Non-canonical linear program relaxation