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| Gale-Shapleyアルゴリズム× | トップ・トレーディング・サイクル× | |
|---|---|---|
| 分野 | ゲーム理論 | ゲーム理論 |
| 系統 | Machine learning | Machine learning |
| 提唱年≠ | 1962 | 1974 |
| 提唱者≠ | David Gale, Lloyd Shapley | Lloyd Shapley, Herbert Scarf |
| 種類 | algorithm | algorithm |
| 原典≠ | Gale, D., & Shapley, L. S. (1962). College admissions and the stability of marriage. The American Mathematical Monthly, 69(1), 9-15. DOI ↗ | Shapley, L. S., & Scarf, H. (1974). On cores and indivisibility. Journal of Mathematical Economics, 1(1), 23-37. DOI ↗ |
| 別名 | Stable Marriage Problem, Deferred Acceptance, Two-Sided Matching | TTC, Shapley-Scarf Algorithm, Efficient Exchange |
| 関連 | 4 | 4 |
| 概要≠ | The Gale-Shapley algorithm solves the stable marriage problem: how to match two groups (e.g., medical residents to hospitals, students to schools) such that no pair prefers each other to their assigned partners. Introduced by David Gale and Lloyd Shapley in 1962, the algorithm guarantees a stable matching in polynomial time through a deferred acceptance process where one side proposes sequentially and the other side responds, revising choices as better options arrive. | Top Trading Cycles (TTC) is an algorithm for allocating indivisible goods to agents such that the allocation is Pareto efficient and individually rational. Developed by Lloyd Shapley and Herbert Scarf in 1974, the algorithm identifies cycles of trades in a preference digraph, executes those trades, and iteratively repeats until no further trades are beneficial. TTC is widely used in kidney exchange and housing allocation due to its efficiency and implementation simplicity. |
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