1 research outputs found
Parameterized algorithms for the 2-clustering problem with minimum sum and minimum sum of squares objective functions
In the {\sc Min-Sum 2-Clustering} problem, we are given a graph and a
parameter , and the goal is to determine if there exists a 2-partition of
the vertex set such that the total conflict number is at most , where the
conflict number of a vertex is the number of its non-neighbors in the same
cluster and neighbors in the different cluster. The problem is equivalent to
{\sc 2-Cluster Editing} and {\sc 2-Correlation Clustering} with an additional
multiplicative factor two in the cost function. In this paper we show an
algorithm for {\sc Min-Sum 2-Clustering} with time complexity , where is the number of vertices and .
Particularly, the time complexity is for and
polynomial for , which implies that the problem can be solved
in subexponential time for . We also design a parameterized
algorithm for a variant in which the cost is the sum of the squared
conflict-numbers. For , the algorithm runs in subexponential
time, where .Comment: journal versio