Partition-distance via the assignment problem
Bioinformatics
On constructing an optimal consensus clustering from multiple clusterings
Information Processing Letters
Reconstructing sibling relationships in wild populations
Bioinformatics
A constant-time dynamic storage allocator for real-time systems
Real-Time Systems
Toward a generic evaluation of image segmentation
IEEE Transactions on Image Processing
Improving the extraction and expansion method for large graph coloring
Discrete Applied Mathematics
Memetic search for the max-bisection problem
Computers and Operations Research
| Hi-index | 0.04 |
A K-partition of a set S is a splitting of S into K non-overlapping classes that cover all elements of S. Numerous practical applications dealing with data partitioning or clustering require computing the distance between two partitions. Previous articles proved that one can compute it in polynomial time-minimum O(|S|+K^2) and maximum O(|S|+K^3)-using a reduction to the linear assignment problem. We propose several conditions for which the partition distance can be computed in O(|S|) time. In practical terms, this computation can be done in O(|S|) time for any two relatively resembling partitions (i.e. with distance less than |S|5) except specially constructed cases. Finally, we prove that, even if there is a bounded number of classes for which the proposed conditions are not satisfied, one can still preserve the linear complexity by exploiting decomposition properties of the similarity matrix.