Journal of Combinatorial Optimization

, Volume 26, Issue 2, pp 310–332

The nearest neighbor Spearman footrule distance for bucket, interval, and partial orders

Authors

  • Franz J. Brandenburg
    • Faculty of Computer Science and MathematicsUniversity of Passau
    • Faculty of Computer Science and MathematicsUniversity of Passau
  • Andreas Hofmeier
    • Faculty of Computer Science and MathematicsUniversity of Passau
Article

DOI: 10.1007/s10878-012-9467-x

Cite this article as:
Brandenburg, F.J., Gleißner, A. & Hofmeier, A. J Comb Optim (2013) 26: 310. doi:10.1007/s10878-012-9467-x

Abstract

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 NP-hard, 4-approximable and fixed-parameter tractable.

Moreover, in contrast to the well-known efficient solution of the rank aggregation problem for total orders, we prove the NP-completeness for bucket orders and establish a 4-approximation.

Keywords

RankingRank aggregationPartial ordersSpearman footrule distanceFixed-parameter tractability

Copyright information

© Springer Science+Business Media, LLC 2012