
On the Complexity of Solution Extension of Optimization Problems
The question if a given partial solution to a problem can be extended re...
read it

Subset Feedback Vertex Set on Graphs of Bounded Independent Set Size
The (Weighted) Subset Feedback Vertex Set problem is a generalization of...
read it

Homomorphism Extension
We define the Homomorphism Extension (HomExt) problem: given a group G, ...
read it

Multistage Graph Problems on a Global Budget
Timeevolving or temporal graphs gain more and more popularity when stud...
read it

Multistage Problems on a Global Budget
Timeevolving or temporal graphs gain more and more popularity when stud...
read it

Constructing bounded degree graphs with prescribed degree and neighbor degree sequences
Let D = d_1, d_2, …, d_n and F = f_1, f_2,…, f_n be two sequences of pos...
read it

The generalized vertex cover problem and some variations
In this paper we study the generalized vertex cover problem (GVC), which...
read it
Extension of vertex cover and independent set in some classes of graphs and generalizations
We consider extension variants of the classical graph problems Vertex Cover and Independent Set. Given a graph G=(V,E) and a vertex set U ⊆ V, it is asked if there exists a minimal vertex cover (resp. maximal independent set) S with U⊆ S (resp. U ⊇ S). Possibly contradicting intuition, these problems tend to be NPhard, even in graph classes where the classical problem can be solved in polynomial time. Yet, we exhibit some graph classes where the extension variant remains polynomialtime solvable. We also study the parameterized complexity of these problems, with parameter U, as well as the optimality of simple exact algorithms under the ExponentialTime Hypothesis. All these complexity considerations are also carried out in very restricted scenarios, be it degree or topological restrictions (bipartite, planar or chordal graphs). This also motivates presenting some explicit branching algorithms for degreebounded instances. We further discuss the price of extension, measuring the distance of U to the closest set that can be extended, which results in natural optimization problems related to extension problems for which we discuss polynomialtime approximability.
READ FULL TEXT
Comments
There are no comments yet.