NP-completeness Results for Graph Burning on Geometric Graphs

03/17/2020
by   Arya Tanmay Gupta, et al.
0

Graph burning runs on discrete time steps. The aim of the graph burning problem is to burn all the vertices in a given graph in the least amount of time steps. The least number of required time steps is known to be the burning number of the graph. The spread of social influence, an alarm, or a social contagion can be modeled using graph burning. The less the burning number, the quick the spread. Computationally, graph burning is hard. It has already been proved that burning of path forests, spider graphs, and trees with maximum degree three are NP-Complete. In this work we study graph burning on geometric graphs and show NP-completeness results on several sub classes. More precisely, we show burning problem to be NP-complete on interval graph, permutation graph and disk graph.

READ FULL TEXT

Authors

page 1

page 2

page 3

page 4

10/03/2020

Burning Geometric Graphs

A procedure called graph burning was introduced to facilitate the modell...
12/23/2019

On the Burning Number of p-Caterpillars

The burning number is a recently introduced graph parameter indicating t...
02/25/2022

Making Life More Confusing for Firefighters

It is well known that fighting a fire is a hard task. The Firefighter pr...
03/06/2019

Proving the NP-completeness of optimal moral graph triangulation

Moral graphs were introduced in the 1980s as an intermediate step when t...
01/09/2019

On NP-completeness of the cell formation problem

In the current paper we provide a proof of NP-completeness for the CFP p...
03/03/2018

Path Puzzles: Discrete Tomography with a Path Constraint is Hard

We prove that path puzzles with complete row and column information--or ...
01/09/2018

NP-Completeness and Inapproximability of the Virtual Network Embedding Problem and Its Variants

Many resource allocation problems in the cloud can be described as a bas...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.