Skip to main content
SpringerLink
Log in

Non-preemptive Tree Packing

  • Conference paper
  • First Online:
Combinatorial Algorithms (IWOCA 2021)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12757))

Included in the following conference series:

  • 871 Accesses

Abstract

An instance of the non-preemptive tree packing problem consists of an undirected graph \(G=(V,E)\) together with a weight w(e) for every edge \(e\in E\). The goal is to activate every edge e for some time interval of length w(e), such that the activated edges keep G connected for the longest possible overall time.

We derive a variety of results on this problem. The problem is strongly NP-hard even on graphs of treewidth 2, and it does not allow a polynomial time approximation scheme (unless P = NP). Furthermore, we discuss the performance of a simple greedy algorithm, and we construct and analyze a number of parameterized and exact algorithms.

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. Akiyama, T., Nishizeki, T., Saito, N.: NP-completeness of the Hamiltonian cycle problem for bipartite graphs. J. Inf. Process. 3, 73–76 (1980)

    MathSciNet  MATH  Google Scholar 

  2. Barahona, F.: Packing spanning trees. Math. Oper. Res. 20, 104–115 (1995)

    Article  MathSciNet  Google Scholar 

  3. Cunningham, W.H.: Optimal attack and reinforcement of a network. J. ACM 32, 549–561 (1985)

    Article  MathSciNet  Google Scholar 

  4. Edmonds, J.: Minimum partition of a matroid into independent subsets. J. Res. Natl. Bur. Stand. 69, 67–72 (1965)

    Article  MathSciNet  Google Scholar 

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

    MATH  Google Scholar 

  6. Nash-Williams, C.S.J.A.: Edge-disjoint spanning trees of finite graphs. J. Lond. Math. Soc. 36, 445–450 (1961)

    Article  MathSciNet  Google Scholar 

  7. Palmer, E.M.: On the spanning tree packing number of a graph: a survey. Discret. Math. 230, 13–21 (2001)

    Article  MathSciNet  Google Scholar 

  8. West, D.B.: Introduction to Graph Theory. Pearson College Div (2000)

    Google Scholar 

Download references

Acknowledgements

Stefan Lendl and Lasse Wulf acknowledge the support of the Austrian Science Fund (FWF): W1230. Gerhard Woeginger acknowledges support by the DFG RTG 2236 “UnRAVeL”.

Author information

Authors and Affiliations

  1. Department of Operations and Information Systems, University of Graz, Graz, Austria

    Stefan Lendl

  2. Department of Computer Science, RWTH Aachen, Aachen, Germany

    Gerhard Woeginger

  3. Institute of Discrete Mathematics, Graz University of Technology, Graz, Austria

    Lasse Wulf

Authors
  1. Stefan Lendl
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Gerhard Woeginger
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Lasse Wulf
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Lasse Wulf .

Editor information

Editors and Affiliations

  1. University of Ottawa, Ottawa, ON, Canada

    Paola Flocchini

  2. University of Ottawa, Ottawa, ON, Canada

    Lucia Moura

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

Lendl, S., Woeginger, G., Wulf, L. (2021). Non-preemptive Tree Packing. In: Flocchini, P., Moura, L. (eds) Combinatorial Algorithms. IWOCA 2021. Lecture Notes in Computer Science(), vol 12757. Springer, Cham. https://doi.org/10.1007/978-3-030-79987-8_32

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-79987-8_32

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-79986-1

  • Online ISBN: 978-3-030-79987-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation