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- W1576341482 abstract "For a set $A$ of $n$ people and a set $B$ of $m$ items, with each person having a preference list that ranks all items from most wanted to least wanted, we consider the problem of matching every person with a unique item. A matching $M$ is called $epsilon$-popular if for any other matching $M'$, the number of people who prefer $M'$ to $M$ is at most $epsilon n$ plus the number of those who prefer $M$ to $M'$. In 2006, Mahdian showed that when randomly generating people's preference lists, if $m/n > 1.42$, then a 0-popular matching exists with $1-o(1)$ probability; and if $m/n 1-epsilon$, then an $epsilon$-popular matching exists with $1-o(1)$ probability (upper bound); and if $alpha(1-e^{-(1+e^{1/alpha})/alpha}) < 1-2epsilon$, then an $epsilon$-popular matching exists with $o(1)$ probability (lower bound)." @default.
- W1576341482 created "2016-06-24" @default.
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- W1576341482 date "2014-10-25" @default.
- W1576341482 modified "2023-09-27" @default.
- W1576341482 title "Random Almost-Popular Matchings" @default.
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