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| Top Trading Cycles× | Gale-Shapleyn algoritmi× | |
|---|---|---|
| Tieteenala | Peliteoria | Peliteoria |
| Menetelmäperhe | Machine learning | Machine learning |
| Syntyvuosi≠ | 1974 | 1962 |
| Kehittäjä≠ | Lloyd Shapley, Herbert Scarf | David Gale, Lloyd Shapley |
| Tyyppi | algorithm | algorithm |
| Alkuperäislähde≠ | Shapley, L. S., & Scarf, H. (1974). On cores and indivisibility. Journal of Mathematical Economics, 1(1), 23-37. DOI ↗ | Gale, D., & Shapley, L. S. (1962). College admissions and the stability of marriage. The American Mathematical Monthly, 69(1), 9-15. DOI ↗ |
| Rinnakkaisnimet | TTC, Shapley-Scarf Algorithm, Efficient Exchange | Stable Marriage Problem, Deferred Acceptance, Two-Sided Matching |
| Liittyvät | 4 | 4 |
| Tiivistelmä≠ | 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. | 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. |
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