# On-line algorithms for weighted matching and stable marriages

 Title On-line algorithms for weighted matching and stable marriages Publication Type Reports Year of Publication 1990 Authors Khuller S, Mitchell SG, Vazirani VV Date Published 1990/// Institution Cornell University Abstract We give an on-line deterministic algorithm for the bipartite weighted matching problem that achieves a competitive ratio of $O(n)$. In fact, this algorithm is almost optimal - the lower bound on the performance ratio of any deterministic online algorithm is $\Omega (n/ \sqrt{log n})$. We also study the stable marriage problem, where we are interested in the number of unstable pairs produced. We show that the simple "first come, first served" deterministic algorithm yields on the average $O(n$ log $n$) unstable pairs, but in the worst case no deterministic or randomized on-line algorithm can do better that $\Omega(n^{2})$ unstable pairs.