Conference Paper

How similarity helps to efficiently compute Kemeny rankings.

DOI: 10.1145/1558013.1558104 Conference: 8th International Joint Conference on Autonomous Agents and Multiagent Systems (AAMAS 2009), Budapest, Hungary, May 10-15, 2009, Volume 1
Source: DBLP

ABSTRACT The computation of Kemeny rankings is central to many applications in the context of rank aggregation. Unfortu- nately, the problem is NP-hard. We show that the Kemeny score (and a corresponding Kemeny ranking) of an election can be computed efficiently whenever the average pairwise distance between two input votes is not too large. In other words, Kemeny Score is fixed-parameter tractable with respect to the parameter "average pairwise Kendall-Tau dis- tance da". We describe a fixed-parameter algorithm with running time 16� d a� · poly. Moreover, we extend our stud- ies to the parameters "maximum range" and "average range" of positions a candidate takes in the input votes. Whereas Kemeny Score remains fixed-parameter tractable with re- spect to the parameter "maximum range", it becomes NP- complete in case of an average range value of two. This excludes fixed-parameter tractability with respect to the pa- rameter "average range" unless P=NP.

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