Approximating Independent Set and Dominating Set on VPG graphs

04/16/2020
by   Esther Galby, et al.
0

We consider Independent Set and Dominating Set restricted to VPG graphs (or, equivalently, string graphs). We show that they both remain 𝖭𝖯-hard on B_0-VPG graphs admitting a representation such that each grid-edge belongs to at most one path and each horizontal path has length at most two. On the other hand, combining the well-known Baker's shifting technique with bounded mim-width arguments, we provide simple PTASes on VPG graphs admitting a representation such that each grid-edge belongs to at most t paths and the length of the horizontal part of each path is at most c, for some c ≥ 1.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
08/30/2017

A Note on Approximating Weighted Independence on Intersection Graphs of Paths on a Grid

A graph G is called B_k-VPG, for some constant k≥ 0, if it has a string ...
research
03/08/2022

Edge Intersection Graphs of Paths on a Triangular Grid

We introduce a new class of intersection graphs, the edge intersection g...
research
01/31/2020

Algorithmic Aspects of Some Variants of Domination in Graphs

A set S ⊆ V is a dominating set in G if for every u ∈ V ∖ S, there exist...
research
08/01/2023

Minimum k-Hop Dominating Sets in Grid Graphs

Given a graph G, the k-hop dominating set problem asks for a vertex subs...
research
09/11/2019

Independent Domination in Directed Graphs

In this paper we initialize the study of independent domination in direc...
research
07/06/2021

Twin-width and polynomial kernels

We study the existence of polynomial kernels, for parameterized problems...
research
10/12/2019

Independent Dominating Sets in Directed Graphs

In this paper, we study independent domination in directed graphs, which...

Please sign up or login with your details

Forgot password? Click here to reset