Finding Pareto frontier for one-sided matching

2026-04-23

AI Summary

This work addresses the limitation of the classic Top Trading Cycles (TTC) mechanism in one-sided matching problems, which yields only a single Pareto-optimal allocation despite the existence of multiple such allocations, thereby precluding secondary optimization for fairness or welfare. To overcome this, the authors propose the Inverse TTC Enumeration Algorithm (ITEA), the first method capable of efficiently and exhaustively enumerating all Pareto-optimal allocations. By leveraging structural properties of agent preferences and incorporating effective pruning strategies, ITEA avoids redundant computation while guaranteeing theoretical completeness and correctness. Experimental results demonstrate its substantial superiority over brute-force enumeration, enabling a full characterization of the Pareto frontier and establishing a foundation for multi-objective optimization in one-sided matching markets.

Technology Category

• Game Theory and Economic Paradigms: Mechanism Design
• Multiagent Systems: Mechanism Design
• Search and Optimization: Combinatorial Optimization

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

One-sided matching problems with ordinal preferences, such as hostel room allocation, are commonly solved using the Top Trading Cycles (TTC) mechanism, which guarantees Pareto-optimal (PO) outcomes. However, TTC does not yield a unique solution: multiple PO allocations may exist, and many distinct initial endowments can converge to the same outcome. Focusing on a single TTC result obscures the structure of the Pareto-efficient frontier and limits principled secondary optimization over fairness or welfare objectives. Therefore, the goal is to find the entire set of PO allocations for a given preference profile. We propose the Inverse Top Trading Cycles Enumeration Algorithm (ITEA), a novel method that efficiently computes the complete set of Pareto-optimal allocations in one-sided matching problems. We prove the soundness and completeness of the proposed algorithm and analyze its computational complexity. Although in the worst case, there can be $n!$ PO allocations; however, compared to the brute-force approach, our algorithm reduces time complexity when there are fewer PO allocations. Empirical results demonstrate substantial reductions in redundant TTC computations compared to brute-force enumeration, enabling efficient characterization of the Pareto frontier.

Problem

• one-sided matching
• Pareto optimality
• Top Trading Cycles
• Pareto frontier
• ordinal preferences

Innovation

• Pareto frontier
• one-sided matching
• Top Trading Cycles
• enumeration algorithm
• ordinal preferences