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

  • Authors:
  • Don Coppersmith;Lisa Fleischer;Atri Rudra

  • Affiliations:
  • Center for Communication Research, IDA, Princeton, NJ;IBM TJ Watson Research Center, Yorktown Heights, NY;University of Washington, Seattle, WA

  • Venue:
  • SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
  • Year:
  • 2006

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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 feedback arc set problem in such weighted tournaments include feedback arc set problem in unweighted tournaments and rank aggregation. Finally, for any constant ε 0, we exhibit an infinite family of (unweighted) tournaments for which the above algorithm (irrespective of how ties are broken) has an approximation ratio of 5 - ε.