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

Authors:
Don Coppersmith;Lisa K. Fleischer;Atri Rurda
Affiliations:
IDA Center for Communications Research, Princeton, NJ;Dartmouth College, Hanover, NH;University at Buffalo, The State University of New York, Buffalo, NY
Venue:
ACM Transactions on Algorithms (TALG)
Year:
2010

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Abstract

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 probability constraints (for any pair of vertices u and v, wuv+wvu=1). Special cases of the feedback arc set problem in such weighted tournaments include the feedback arc set problem in unweighted tournaments and rank aggregation. To complement the upper bound, for any constant ε0, we exhibit an infinite family of (unweighted) tournaments for which the aforesaid algorithm (irrespective of how ties are broken) has an approximation ratio of 5-ε.