The nearest neighbor Spearman footrule distance for bucket, interval, and partial orders
 Franz J. Brandenburg,
 Andreas Gleißner,
 Andreas Hofmeier
 … show all 3 hide
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Comparing and ranking information is an important topic in social and information sciences, and in particular on the web. Its objective is to measure the difference of the preferences of voters on a set of candidates and to compute a consensus ranking. Commonly, each voter provides a total order of all candidates. Recently, this approach was generalized to bucket orders, which allow ties.
In this work we further generalize and consider total, bucket, interval and partial orders. The disagreement between two orders is measured by the nearest neighbor Spearman footrule distance, which has not been studied so far. For two bucket orders and for a total and an interval order the nearest neighbor Spearman footrule distance is shown to be computable in linear time, whereas for a total and a partial order the computation is NPhard, 4approximable and fixedparameter tractable.
Moreover, in contrast to the wellknown efficient solution of the rank aggregation problem for total orders, we prove the NPcompleteness for bucket orders and establish a 4approximation.
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 Title
 The nearest neighbor Spearman footrule distance for bucket, interval, and partial orders
 Journal

Journal of Combinatorial Optimization
Volume 26, Issue 2 , pp 310332
 Cover Date
 20130801
 DOI
 10.1007/s108780129467x
 Print ISSN
 13826905
 Online ISSN
 15732886
 Publisher
 Springer US
 Additional Links
 Topics
 Keywords

 Ranking
 Rank aggregation
 Partial orders
 Spearman footrule distance
 Fixedparameter tractability
 Industry Sectors
 Authors

 Franz J. Brandenburg ^{(1)}
 Andreas Gleißner ^{(1)}
 Andreas Hofmeier ^{(1)}
 Author Affiliations

 1. Faculty of Computer Science and Mathematics, University of Passau, 94030, Passau, Germany