TY - GEN
T1 - Burning Grids and Intervals
AU - Gupta, Arya Tanmay
AU - Lokhande, Swapnil A.
AU - Mondal, Kaushik
N1 - Publisher Copyright:
© 2021, Springer Nature Switzerland AG.
PY - 2021/1/1
Y1 - 2021/1/1
N2 - Graph burning runs on discrete time steps. The aim is to burn all the vertices in a given graph in the least number of time steps. This number 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 faster the spread. Optimal burning of general graphs is NP-Hard. There is a 3-approx-imation algorithm to burn general graphs where as better approximation factors are there for many sub classes. Here we study burning of grids; provide a lower bound for burning arbitrary grids and a 2-approximation algorithm for burning square grids. On the other hand, burning path forests, spider graphs, and trees with maximum degree three is already known to be NP-Complete. In this article we show burning problem to be NP-Complete on connected interval graphs.
AB - Graph burning runs on discrete time steps. The aim is to burn all the vertices in a given graph in the least number of time steps. This number 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 faster the spread. Optimal burning of general graphs is NP-Hard. There is a 3-approx-imation algorithm to burn general graphs where as better approximation factors are there for many sub classes. Here we study burning of grids; provide a lower bound for burning arbitrary grids and a 2-approximation algorithm for burning square grids. On the other hand, burning path forests, spider graphs, and trees with maximum degree three is already known to be NP-Complete. In this article we show burning problem to be NP-Complete on connected interval graphs.
UR - http://www.scopus.com/inward/record.url?scp=85101312484&partnerID=8YFLogxK
U2 - 10.1007/978-3-030-67899-9_6
DO - 10.1007/978-3-030-67899-9_6
M3 - Conference contribution
AN - SCOPUS:85101312484
SN - 9783030678982
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 66
EP - 79
BT - Algorithms and Discrete Applied Mathematics - 7th International Conference, CALDAM 2021, Proceedings
A2 - Mudgal, Apurva
A2 - Subramanian, C. R.
PB - Springer Science and Business Media Deutschland GmbH
T2 - 7th International Conference on Algorithms and Discrete Applied Mathematics, CALDAM 2021
Y2 - 11 February 2021 through 13 February 2021
ER -