DeepAI AI Chat
Log In Sign Up

Locally checkable problems parameterized by clique-width

by   Narmina Baghirova, et al.
University of Buenos Aires
University of Fribourg

We continue the study initiated by Bonomo-Braberman and Gonzalez in 2020 on r-locally checkable problems. We propose a dynamic programming algorithm that takes as input a graph with an associated clique-width expression and solves a 1-locally checkable problem under certain restrictions. We show that it runs in polynomial time in graphs of bounded clique-width, when the number of colors of the locally checkable problem is fixed. Furthermore, we present a first extension of our framework to global properties by taking into account the sizes of the color classes, and consequently enlarge the set of problems solvable in polynomial time with our approach in graphs of bounded clique-width. As examples, we apply this setting to show that, when parameterized by clique-width, the [k]-Roman domination problem is FPT, and the k-community problem, Max PDS and other variants are XP.


page 1

page 2

page 3

page 4


On the Clique-Width of Unigraphs

Clique-width is a well-studied graph parameter. For graphs of bounded cl...

On d-stable locally checkable problems on bounded mim-width graphs

In this paper we continue the study of locally checkable problems under ...

Clique-Width and Directed Width Measures for Answer-Set Programming

Disjunctive Answer Set Programming (ASP) is a powerful declarative progr...

The Reward-Penalty-Selection Problem

The Set Cover Problem (SCP) and the Hitting Set Problem (HSP) are well-s...

Clique-Width of Point Configurations

While structural width parameters (of the input) belong to the standard ...

Fast exact algorithms for some connectivity problems parametrized by clique-width

Given a clique-width expression of a graph G of clique-width k, we provi...

A Survey on Parameterized Inapproximability: k-Clique, k-SetCover, and More

In the past a few years, many interesting inapproximability results have...