TY - JOUR
AU - Suchý, Ondřej
AB - A balanced partition is a clustering of a graph into a given number of equal-sized parts. For instance, the Bisection problem asks to remove at most k edges in order to partition the vertices into two equal-sized parts. We prove that Bisection is FPT for the distance to constant cliquewidth if we are given the deletion set. This implies FPT algorithms for some well-studied parameters such as cluster vertex deletion number and feedback vertex set. However, we show that Bisection does not admit polynomial-size kernels for these parameters. For the Vertex
Bisection problem, vertices need to be removed in order to obtain two equal-sized parts. We show that this problem is FPT for the number of removed vertices k if the solution cuts the graph into a constant number c of connected components. The latter condition is unavoidable, since we also prove that Vertex
Bisection is W[1]-hard w.r.t. (k,c). Our algorithms for finding bisections can easily be adapted to finding partitions into d equal-sized parts, which entails additional running time factors of n

O(d). We show that a substantial speed-up is unlikely since the corresponding task is W[1]-hard w.r.t. d, even on forests of maximum degree two. We can, however, show that it is FPT for the vertex cover number.
TI - On the Parameterized Complexity of Computing Balanced Partitions in Graphs
JO - Theory of Computing Systems
DO - 10.1007/s00224-014-9557-5
DA - 2014-07-08
UR - https://www.deepdyve.com/lp/springer-journals/on-the-parameterized-complexity-of-computing-balanced-partitions-in-J4if7KhiCC
SP - 1
EP - 35
VL - 57
IS - 1
DP - DeepDyve
ER -