השוואת שיטות

	אלגוריתם גייל-שפלי	Top Trading Cycles
תחום	תורת המשחקים	תורת המשחקים
משפחה	Machine learning	Machine learning
שנת המקור	1962	1974
הוגה השיטה	David Gale, Lloyd Shapley	Lloyd Shapley, Herbert Scarf
סוג	algorithm	algorithm
מקור מכונן	Gale, D., & Shapley, L. S. (1962). College admissions and the stability of marriage. The American Mathematical Monthly, 69(1), 9-15.	Shapley, L. S., & Scarf, H. (1974). On cores and indivisibility. Journal of Mathematical Economics, 1(1), 23-37.
כינויים	Stable Marriage Problem, Deferred Acceptance, Two-Sided Matching	TTC, Shapley-Scarf Algorithm, Efficient Exchange
קשורות	4	4
תקציר	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.