Technology Category
Game Theory and Economic Paradigms: Mechanism DesignMultiagent Systems: Mechanism DesignSearch and Optimization: Combinatorial Optimization
Finding Pareto frontier for one-sided matching
🤖 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
Application Category
📝 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
Research questions and friction points this paper is trying to address.
one-sided matching
Pareto optimality
Top Trading Cycles
Pareto frontier
ordinal preferences
Innovation
Methods, ideas, or system contributions that make the work stand out.
Pareto frontier
one-sided matching
Top Trading Cycles
enumeration algorithm
ordinal preferences
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