Skip to main content
SpringerLink
Log in

Burning Grids and Intervals

  • Conference paper
  • First Online:
Algorithms and Discrete Applied Mathematics (CALDAM 2021)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12601))

Included in the following conference series:

Abstract

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.

A.T. Gupta—This study was conducted when A T Gupta was affiliated with the Indian Institute of Information Technology Vadodara, India.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 79.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 99.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. S̃imon, M., Huraj, L., Dirgovã Luptãkovã, I., Pospíchal, J.: Heuristics for spreading alarm throughout a network. Appl. Sci. 9(16), 3269 (2019)

    Google Scholar 

  2. Alon, N., PraLat, P., Wormald, N.: Cleaning regular graphs with brushes. SIAM J. Disc. Math. 23(1), 233–250 (2009)

    Article  MathSciNet  Google Scholar 

  3. Balogh, J., Bollobás, B., Morris, R.: Graph bootstrap percolation. Random Struct. Algorithms 41(4), 413–440 (2012)

    Article  MathSciNet  Google Scholar 

  4. Banerjee, S., Gopalan, A., Das, A., Shakkottai, S.: Epidemic spreading with external agents. IEEE Trans. Inf. Theory 60, 06 (2012)

    MathSciNet  MATH  Google Scholar 

  5. Bessy, S., Bonato, A., Janssen, J., Rautenbach, D., Roshanbin, E.: Burning a graph is hard. Disc. Appl. Math. 232(C), 73–87 (2017)

    Article  MathSciNet  Google Scholar 

  6. Bessy, S., Bonato, A., Janssen, J., Rautenbach, D., Roshanbin, E.: Bounds on the burning number. Disc. Appl. Math. 235, 16–22 (2018)

    Article  MathSciNet  Google Scholar 

  7. Bonato, A., Janssen, J., Roshanbin, E.: How to burn a graph. Internet Math. 12(1–2), 85–100 (2016)

    Article  MathSciNet  Google Scholar 

  8. Bonato, A., Kamali, S.: Approximation algorithms for graph burning. In: Gopal, T.V., Watada, J. (eds.) TAMC 2019. LNCS, vol. 11436, pp. 74–92. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-14812-6_6

    Chapter  Google Scholar 

  9. Bonato, A., Lidbetter, T.: Bounds on the burning numbers of spiders and path-forests. Theor. Comput. Scie. 794, 12–19 (2019)

    Article  MathSciNet  Google Scholar 

  10. Bonato, A., Janssen, J., Roshanbin, E.: Burning a graph as a model of social contagion. In: Bonato, A., Graham, F.C., Prałat, P. (eds.) WAW 2014. LNCS, vol. 8882, pp. 13–22. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-13123-8_2

    Chapter  MATH  Google Scholar 

  11. Das, S., Dev, S.R., Sadhukhan, A., Sahoo, U., Sen, S.: Burning spiders. In: Panda, B.S., Goswami, P.P. (eds.) CALDAM 2018. LNCS, vol. 10743, pp. 155–163. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-74180-2_13

    Chapter  Google Scholar 

  12. Finbow, S., Macgillivray, G.: The firefighter problem: a survey of results, directions and questions. Australas. J. Comb. [Electron. only] 43, 57–78 (2009)

    MathSciNet  MATH  Google Scholar 

  13. Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman & Co., New York (1979)

    MATH  Google Scholar 

  14. Gupta, A.T., Lokhande, S.A., Mondal, K.: Np-completeness results for graph burning on geometric graphs. arXiv: 2003.07746 (2020)

  15. Kamali, S., Miller, A., Zhang, K.: Burning two worlds. In: SOFSEM (2020)

    Google Scholar 

  16. Kare, A.S., Vinod Reddy, I.: Parameterized algorithms for graph burning problem. In: Colbourn, C.J., Grossi, R., Pisanti, N. (eds.) IWOCA 2019. LNCS, vol. 11638, pp. 304–314. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-25005-8_25

    Chapter  MATH  Google Scholar 

  17. Kempe, D., Kleinberg, J., Tardos, É.: Maximizing the spread of influence through a social network. In: ACM SIGKDD, pp. 137–146. Association for Computing Machinery, New York (2003)

    Google Scholar 

  18. Kempe, D., Kleinberg, J., Tardos, É.: Influential nodes in a diffusion model for social networks. In: Caires, L., Italiano, G.F., Monteiro, L., Palamidessi, C., Yung, M. (eds.) ICALP 2005. LNCS, vol. 3580, pp. 1127–1138. Springer, Heidelberg (2005). https://doi.org/10.1007/11523468_91

    Chapter  Google Scholar 

  19. Kramer, A.D.I., Guillory, J.E., Hancock, J.T.: Experimental evidence of massive-scale emotional contagion through social networks. Proc. Natl. Acad. Sci. 111(24), 8788–8790 (2014)

    Article  Google Scholar 

  20. Simon, M., Huraj, L., Dirgova, L., Pospichal, J.: How to burn a network or spread alarm. MENDEL 25(2), 11–18 (2019)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Michigan State University, East Lansing, MI, USA

    Arya Tanmay Gupta

  2. Indian Institute of Information Technology Vadodara, Gandhinagar, India

    Swapnil A. Lokhande

  3. Indian Institute of Technology Ropar, Rupnagar, India

    Kaushik Mondal

Authors
  1. Arya Tanmay Gupta
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Swapnil A. Lokhande
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Kaushik Mondal
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Arya Tanmay Gupta or Kaushik Mondal .

Editor information

Editors and Affiliations

  1. Indian Institute of Technology Ropar, Rupnagar, India

    Apurva Mudgal

  2. Institute of Mathematical Sciences, Chennai, India

    C. R. Subramanian

Rights and permissions

Reprints and permissions

Copyright information

© 2021 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Gupta, A.T., Lokhande, S.A., Mondal, K. (2021). Burning Grids and Intervals. In: Mudgal, A., Subramanian, C.R. (eds) Algorithms and Discrete Applied Mathematics. CALDAM 2021. Lecture Notes in Computer Science(), vol 12601. Springer, Cham. https://doi.org/10.1007/978-3-030-67899-9_6

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-67899-9_6

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-67898-2

  • Online ISBN: 978-3-030-67899-9

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation