Stable Marrige Problem

In: Computers and Technology

Submitted By asdfasdf123
Words 948
Pages 4
Stable marriage problem
Av Johan Magnusson, SA11 2011-11-07

Inledning Rapporten som följer handlar om det klassiska Stable marriage problemet, SMP. SMP innebär att man låter männen ranka kvinnorna från mest tänkbar till minst tänkbar och vice versa. Utifrån det skall man para ihop männen med kvinnorna på bästa tänkbara sätt. Bästa tänkbara sätt innebär ett stabilt förhållande samt inga singlar. Ett problem som kan liknas vid första valet av sjukhus för läkarstudenter. Rapporten presenterar problemet samt Gale – Shapley algoritmen jämfört med en rekursiv algoritm för att skapa stabila förhållanden. Historia och lösningar Stable marriage problemet är ett välkänt mattematiskt matchnings problem, där första lösningen lanserades av David Gale och Lloyd Shapley (1962). Problemet innebär att man ska hitta de bästa tänkbara paren av n kvinnor och n män. Varje man och varje kvinna listar det motsatta könet från den det helst vill paras ihop med till den de minst vill paras ihop med. Man ska utifrån listorna bilda par där det inte kan finnas ett par som skulle passa bättre ihop än det givna. Förhållandet mellan paren anses vara stabilt när det inte finns något blockerande par, dvs. när det finns möjliga byten mellan par som rankat en partner högre än den nuvarande. Det är bevisat av Gale och Shapley (1962) att i varje SMP med lika många män som kvinnor finns det minst en stabil lösning. Problemet är vanligt förekommande när nyexaminerade läkarstudenter ska välja sitt första sjukhus. Gale – Shapley algoritmen utförs i flera steg. I det första steget friar männen till de kvinnorna de har rankat högst. Om flera män friar till samma kvinna accepterar hon den man hon rankat högst och avvisar den lägre rankade mannen. I nästa steg friar de männen som blev avvisade till den kvinna de rankat som nummer två. Om kvinnan är ledig accepterar hon, om hon redan har en partner väljer…...

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