Rank aggregation methods for the Web
Proceedings of the 10th international conference on World Wide Web
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Aggregating inconsistent information: ranking and clustering
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Deterministic pivoting algorithms for constrained ranking and clustering problems
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Aggregation of partial rankings, p-ratings and top-m lists
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
| Hi-index | 0.89 |
In the classic rank aggregation (RA) problem, we are given L input lists with potentially inconsistent orders of n elements; our goal is to find a single order of all elements that minimizes the total number of disagreements with the given orders. The problem is well known to be NP-hard, already for L=4. We consider a generalization of RA, where each list is associated with a set of orderings, and our goal is to choose one ordering per list and to find a permutation of the elements that minimizes the total disagreements with the chosen orderings. For the case in which the lists completely overlap, i.e. each list contains all n elements, we show that a simple Greedy algorithm yields a (2-2/L)-approximation for generalized RA. The case in which the lists only partially overlap, i.e. each list contains a subset of the n elements, is much harder to approximate. In fact, we show that RA with multiple orderings per list and partial overlaps cannot be approximated within any bounded ratio.