4,592 research outputs found
On domination problems for permutation and other graphs
AbstractThere is an increasing interest in results on the influence of restricting NP-complete graph problems to special classes of perfect graphs as, e.g., permutation graphs. It was shown that several problems restricted to permutation graphs are solvable in polynomial time [2, 3, 4, 6, 7, 14, 16].In this paper we give 1.(i) an algorithm with time bound O(n2) for the weighted independent domination problem on permutation graphs (which is an improvement of the O(n3) solution given in [7]);2.(ii) a polynomial time solution for the weighted feedback vertex set problem on permutation graphs;3.(iii) an investigation of (weighted) dominating clique problems for several graph classes including an NP-completeness result for weakly triangulated graphs as well as polynomial time bounds
On Directed Feedback Vertex Set parameterized by treewidth
We study the Directed Feedback Vertex Set problem parameterized by the
treewidth of the input graph. We prove that unless the Exponential Time
Hypothesis fails, the problem cannot be solved in time on general directed graphs, where is the treewidth of
the underlying undirected graph. This is matched by a dynamic programming
algorithm with running time .
On the other hand, we show that if the input digraph is planar, then the
running time can be improved to .Comment: 20
A survey on algorithmic aspects of modular decomposition
The modular decomposition is a technique that applies but is not restricted
to graphs. The notion of module naturally appears in the proofs of many graph
theoretical theorems. Computing the modular decomposition tree is an important
preprocessing step to solve a large number of combinatorial optimization
problems. Since the first polynomial time algorithm in the early 70's, the
algorithmic of the modular decomposition has known an important development.
This paper survey the ideas and techniques that arose from this line of
research
Structural Completeness of a Multi-channel Linear System with Dependent Parameters
It is well known that the "fixed spectrum" {i.e., the set of fixed modes} of
a multi-channel linear system plays a central role in the stabilization of such
a system with decentralized control. A parameterized multi-channel linear
system is said to be "structurally complete" if it has no fixed spectrum for
almost all parameter values. Necessary and sufficient algebraic conditions are
presented for a multi-channel linear system with dependent parameters to be
structurally complete. An equivalent graphical condition is also given for a
certain type of parameterization
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