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TR05-131 | 7th November 2005 00:00

Ordering by weighted number of wins gives a good ranking for weighted tournaments



We consider the following simple algorithm for feedback arc set problem in weighted tournaments --- order the vertices by their weighted indegrees. We show that this algorithm has an approximation guarantee of $5$ if the weights satisfy \textit{probability constraints}
(for any pair of vertices $u$ and $v$, $w_{uv}+w_{vu}=1$). Special cases of feedback arc set problem in such weighted tournaments include feedback arc set problem in unweighted tournaments and rank aggregation. Finally, for any constant $\epsilon>0$, we exhibit an infinite family of (unweighted) tournaments for which the above algorithm ({\em irrespective} of how ties are broken) has an approximation ratio of $5-\epsilon$.

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