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In the Categorical Clustering problem, we are given a set of vectors (matrix) A={a_1,ldots,a_n} over Sigma^m, where Sigma is a finite alphabet, and integers k and B. The task is to partition A into k clusters such that the median objective of the clustering in the Hamming norm is at most B. That is, we seek a partition {I_1,ldots,I_k} of {1,ldots,n} and vectors c_1,ldots,c_kinSigma^m such that sum_{i=1}^ksum_{jin I_i}d_h(c_i,a_j)leq B, where d_H(a,b) is the Hamming distance between vectors a and b. Fomin, Golovach, and Panolan [ICALP 2018] proved that the problem is fixed-parameter tractable (for binary case Sigma={0,1}) by giving an algorithm that solves the problem in time 2^{O(Blog B)} (mn)^{O(1)}. We extend this algorithmic result to a popular capacitated clustering model, where in addition the sizes of the clusters should satisfy certain constraints. More precisely, in Capacitated Clustering, in addition, we are given two non-negative integers p and q, and seek a clustering with pleq |I_i|leq q for all iin{1,ldots,k}. Our main theorem is that Capacitated Clustering is solvable in time 2^{O(Blog B)}|Sigma|^B(mn)^{O(1)}. The theorem not only extends the previous algorithmic results to a significantly more general model, it also implies algorithms for several other variants of Categorical Clustering with constraints on cluster sizes.
We develop new algorithmic methods with provable guarantees for feature selection in regard to categorical data clustering. While feature selection is one of the most common approaches to reduce dimensionality in practice, most of the known feature s
We investigate the parameterized complexity of the following edge coloring problem motivated by the problem of channel assignment in wireless networks. For an integer q>1 and a graph G, the goal is to find a coloring of the edges of G with the maximu
An enumeration kernel as defined by Creignou et al. [Theory Comput. Syst. 2017] for a parameterized enumeration problem consists of an algorithm that transforms each instance into one whose size is bounded by the parameter plus a solution-lifting alg
The problem of publishing personal data without giving up privacy is becoming increasingly important. An interesting formalization that has been recently proposed is the $k$-anonymity. This approach requires that the rows of a table are partitioned i
We study two variants of textsc{Maximum Cut}, which we call textsc{Connected Maximum Cut} and textsc{Maximum Minimal Cut}, in this paper. In these problems, given an unweighted graph, the goal is to compute a maximum cut satisfying some connectivity