How similarity helps to efficiently compute Kemeny rankings
AAMAS (1)(2009)
摘要
The computation of Kemeny rankings is central to many applications in the context of rank aggregation. Unfortunately, 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 distance da". We describe a fixed-parameter algorithm with running time 16[da] · poly. Moreover, we extend our studies 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 respect 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 parameter "average range" unless P=NP.
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关键词
fixed-parameter tractable,average pairwise kendall-tau distance,kemeny ranking,maximum range,corresponding kemeny ranking,input vote,average pairwise distance,kemeny score,average range value,average range,np hard problem
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