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arXiv · 1401.5269

Stable Roommates Problem with Random Preferences

Stephan Mertens
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Abstract

The stable roommates problem with $n$ agents has worst case complexity $O(n^2)$ in time and space. Random instances can be solved faster and with less memory, however. We introduce an algorithm that has average time and space complexity $O(n^\frac{3}{2})$ for random instances. We use this algorithm to simulate large instances of the stable roommates problem and to measure the probabilty $p_n$ that a random instance of size $n$ admits a stable matching. Our data supports the conjecture that $p_n = Θ(n^{-1/4})$.

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Stephan Mertens. 2015-01-21. Stable Roommates Problem with Random Preferences. https://doi.org/10.1088/1742-5468%2F2015%2F01%2Fp01020

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