Clustering
Correlation Clustering is a model for clustering data when a binary relationship between data points is known. More precisely, for each pair of points we have two scores measuring the similarity and dissimilarity respectively, of the two points, and we would like to compute an optimal partition where the value of a partition is obtained by summing up scores of pairs involving points from a same cluster and scores of pairs involving points from different clusters. The main difference between Correlation Clustering and, say, k-means is that for the former the number of sets of the solution is not known a priori.
A closely related problem is Consensus Clustering, where we are given a set of partitions and we would like to obtain a partition that best summarizes the input partitions. We have investigate the computational complexity of both problems and we have designed some efficient approximation algorithms.
Data privacy
Recently, we have contributed to the design of parameterized algorithms for the k-anonymity problem and solved some issues related to the computational complexity of this problem.
Graph Decomposition
For some problems, decomposing a graph allows for the application of a divide-and-conquer technique to design efficient algorithms. A kind of decomposition that we have studied is called modular decomposition.
