Ranking chain sum orders

Ranking information is an important topic in information sciences, Internet searching, voting systems, and sports. In the full information approach, a ranking is a total order of the candidates. We compare two rankings by pairwise comparisons under the nearest neighbor Kendall tau distance and study...

Full description

Saved in:
Bibliographic Details
Published in:Theoretical computer science Vol. 636; pp. 66 - 76
Main Authors: Brandenburg, Franz J., Gleißner, Andreas
Format: Journal Article
Language:English
Published: Elsevier B.V 11.07.2016
Subjects:
[formula omitted]-hardness
Agglomeration
Buckets
Chains
Distance measures
Equivalence
Fixed-parameter complexity
Internet
Polynomials
Ranking
Searching
Total and partial orders
NP-hardness
Ranking
Distance measures
Fixed-parameter complexity
Total and partial orders
ISSN:0304-3975, 1879-2294
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Ranking information is an important topic in information sciences, Internet searching, voting systems, and sports. In the full information approach, a ranking is a total order of the candidates. We compare two rankings by pairwise comparisons under the nearest neighbor Kendall tau distance and study the distance and rank aggregation problems. In many settings, the information is incomplete and a ranking is given by a partial order. A bucket order is obtained if a ranking allows ties and treats tied candidates as equivalent. Then the distance and rank aggregation problems can be solved efficiently in almost linear time. A chain sum order is complementary to a bucket order and consists of a set of disjoint total orders. Its width and height is the number and the maximum size of the total orders, respectively. We show that the distance and rank aggregation problems of a total order and a chain sum order of bounded width or of height at most two can be solved in polynomial time and are NP-complete for a total and a chain sum order of height at least 12. Both problems remain NP-complete for a total and a heap order which is the partial order obtained from a single-elimination tournament (in sports). However, the problems are fixed-parameter tractable with respect to the distance and the Ulam distance, but are fixed-parameter intractable with respect to the order dimension.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 23
ISSN:0304-3975
1879-2294
DOI:10.1016/j.tcs.2016.05.026