12 research outputs found
Kernelization and Parameterized Algorithms for 3-Path Vertex Cover
A 3-path vertex cover in a graph is a vertex subset such that every path
of three vertices contains at least one vertex from . The parameterized
3-path vertex cover problem asks whether a graph has a 3-path vertex cover of
size at most . In this paper, we give a kernel of vertices and an
-time and polynomial-space algorithm for this problem, both new
results improve previous known bounds.Comment: in TAMC 2016, LNCS 9796, 201
Faster FPT Algorithm for 5-Path Vertex Cover
The problem of d-Path Vertex Cover, d-PVC lies in determining a subset F of vertices of a given graph G=(V,E) such that G F does not contain a path on d vertices. The paths we aim to cover need not to be induced. It is known that the d-PVC problem is NP-complete for any d >= 2. When parameterized by the size of the solution k, 5-PVC has direct trivial algorithm with O(5^kn^{O(1)}) running time and, since d-PVC is a special case of d-Hitting Set, an algorithm running in O(4.0755^kn^{O(1)}) time is known. In this paper we present an iterative compression algorithm that solves the 5-PVC problem in O(4^kn^{O(1)}) time
Generating faster algorithms for d-Path Vertex Cover
Many algorithms which exactly solve hard problems require branching on more
or less complex structures in order to do their job. Those who design such
algorithms often find themselves doing a meticulous analysis of numerous
different cases in order to identify these structures and design suitable
branching rules, all done by hand. This process tends to be error prone and
often the resulting algorithm may be difficult to implement in practice.
In this work, we aim to automate a part of this process and focus on
simplicity of the resulting implementation.
We showcase our approach on the following problem. For a constant , the
-Path Vertex Cover problem (-PVC) is as follows: Given an undirected
graph and an integer , find a subset of at most vertices of the graph,
such that their deletion results in a graph not containing a path on
vertices as a subgraph. We develop a fully automated framework to generate
parameterized branching algorithms for the problem and obtain algorithms
outperforming those previously known for . E.g., we show that
-PVC can be solved in time