DeepAI AI Chat
Log In Sign Up

The Algorithmic Complexity of Tree-Clique Width

by   Chris Aronis, et al.

Tree-width has been proven to be a useful parameter to design fast and efficient algorithms for intractable problems. However, while tree-width is low on relatively sparse graphs can be arbitrary high on dense graphs. Therefore, we introduce tree-clique width, denoted by tcl(G) for a graph G, a new width measure for tree decompositions. The main aim of such a parameter is to extend the algorithmic gains of tree-width on more structured and dense graphs. In this paper, we show that tree-clique width is NP-complete and that there is no constant-factor approximation algorithm for any constant value c. We also provide algorithms to compute tree-clique width for general graphs and for special graphs such as cographs and permutation graphs. We seek to understand further tree-clique width and its properties and to research whether it can be used as an alternative where tree-width fails.


page 1

page 2

page 3

page 4


Parity Games of Bounded Tree-Depth

The exact complexity of solving parity games is a major open problem. Se...

Maximizing Happiness in Graphs of Bounded Clique-Width

Clique-width is one of the most important parameters that describes stru...

A unified algorithm for colouring graphs of bounded clique-width

Clique-width is one of the graph complexity measures leading to polynomi...

A Unifying Framework for Characterizing and Computing Width Measures

Algorithms for computing or approximating optimal decompositions for dec...

FPT algoritms providing constant ratio approximation of hypertree width parameters for hypergraphs of bounded rank

We propose an algorithm whose input are parameters k and r and a hypergr...

Structured Decompositions: Structural and Algorithmic Compositionality

We introduce structured decompositions: category-theoretic generalizatio...

A framework for minimal hereditary classes of graphs of unbounded clique-width

We create a framework for hereditary graph classes 𝒢^δ built on a two-di...