Faisal Abu-Khzam
Title :
Kernelization
Algorithms
for
Vertex
Cover
in
d-Uniform
Hypergraphs
Abstract :
For a parameterized problem X, a kernelization algorithm is a polynomial-time self
reduction procedure that transforms an arbitrary input instance of X into one whose size is
bounded by a function of the input parameter(s). The resulting instance is called a problem
kernel. In this talk we discuss kernelization algorithms for the Vertex Cover problem. In
short, an input instance of Vertex Cover consists of a graph G together with a positive
integer k, and the target solution is a set of k (or less) vertices whose complement induces
an edge-less subgraph. When G is a d-uniform hypergraph, the problem is also known as dHitting Set. We present a kernelization algorithm for d-Hitting Set that can guarantee a
problem kernel whose cardinality is in O(k^{d-1}).