On the complexity of approximating the independent set problem
Information and Computation
Proof verification and the hardness of approximation problems
Journal of the ACM (JACM)
Robust Clustering by Aggregation and Intersection Methods
KES '08 Proceedings of the 12th international conference on Knowledge-Based Intelligent Information and Engineering Systems, Part III
A Fast Approximation Algorithm for the k Partition-Distance Problem
ICCSA '09 Proceedings of the International Conference on Computational Science and Its Applications: Part II
Multiple data structure discovery through global optimisation, meta clustering and consensus methods
International Journal of Knowledge Engineering and Soft Data Paradigms
A novel hierarchical-clustering-combination scheme based on fuzzy-similarity relations
IEEE Transactions on Fuzzy Systems
An efficient algorithm for computing the distance between close partitions
Discrete Applied Mathematics
Hi-index | 0.89 |
Computing a suitable measure of consensus among several clusterings on the same data is an important problem that arises in several areas such as computational biology and data mining. In this paper, we formalize a set-theoretic model for computing such a similarity measure. Roughly speaking, in this model we have k 1 partitions (clusters) of the same data set each containing the same number of sets and the goal is to align the sets in each partition to minimize a similarity measure. For k=2, a polynomial-time solution was proposed by Gusfield (Information Processing Letters 82 (2002) 159-164). In this paper, we show that the problem is MAX-SNP-hard for k=3 even if each partition in each cluster contains no more than 2 elements and provide a -approximation algorithm for the problem for any k.