Skip to main content
SpringerLink
Log in
SpringerLink
Log in

The Parameterized Complexity of the Induced Matching Problem in Planar Graphs

  • Conference paper
Frontiers in Algorithmics (FAW 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4613))

Included in the following conference series:

Abstract

Given a graph G and an integer k ≥ 0, the NP-complete Induced Matching problem asks for an edge subset M such that M is a matching and no two edges of M are joined by an edge of G. The complexity of this problem on general graphs as well as on many restricted graph classes has been studied intensively. However, little is known about the parameterized complexity of this problem. Our main contribution is to show that Induced Matching, which is W[1]-hard in general, admits a linear problem kernel on planar graphs. Additionally, we generalize a known algorithm for Induced Matching on trees to graphs of bounded treewidth using an improved dynamic programming approach.

Supported by a DAAD-DST exchange program, D/05/57666.

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 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Alber, J., Fan, H., Fellows, M.R., Fernau, H., Niedermeier, R., Rosamond, F.A., Stege, U.: A refined search tree technique for dominating set on planar graphs. Journal of Computer and System Sciences 71(4), 385–405 (2005)

    Article  MATH  Google Scholar 

  2. Alber, J., Fellows, M.R., Niedermeier, R.: Polynomial-time data reduction for dominating set. Journal of the ACM 51(3), 363–384 (2004)

    Article  Google Scholar 

  3. Alber, J., Niedermeier, R.: Improved tree decomposition based algorithms for domination-like problems. In: Rajsbaum, S. (ed.) LATIN 2002. LNCS, vol. 2286, pp. 613–628. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  4. Bodlaender, H.L.: Treewidth: Characterizations, applications, and computations. In: Fomin, F.V. (ed.) WG 2006. LNCS, vol. 4271, pp. 1–14. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  5. Cameron, K.: Induced matchings in intersection graphs. Discrete Mathematics 278(1-3), 1–9 (2004)

    Article  MATH  Google Scholar 

  6. Cameron, K., Sritharan, R., Tang, Y.: Finding a maximum induced matching in weakly chordal graphs. Discrete Mathematics 266(1-3), 133–142 (2003)

    Article  MATH  Google Scholar 

  7. Chen, J., Fernau, H., Kanj, I.A., Xia, G.: Parametric duality and kernelization: lower bounds and upper bounds on kernel size. SIAM Journal on Computing (to appear)

    Google Scholar 

  8. Chlebík, M., Chlebíková, J.: Approximation hardness of dominating set problems. In: Albers, S., Radzik, T. (eds.) ESA 2004. LNCS, vol. 3221, pp. 192–203. Springer, Heidelberg (2004)

    Google Scholar 

  9. Downey, R.G., Fellows, M.R.: Parameterized Complexity. Springer, Heidelberg (1999)

    Google Scholar 

  10. Duckworth, W., Manlove, D., Zito, M.: On the approximability of the maximum induced matching problem. Journal of Discrete Algorithms 3(1), 79–91 (2005)

    Article  MATH  Google Scholar 

  11. Fomin, F.V., Thilikos, D.M.: Fast parameterized algorithms for graphs on surfaces: Linear kernel and exponential speed-up. In: Díaz, J., Karhumäki, J., Lepistö, A., Sannella, D. (eds.) ICALP 2004. LNCS, vol. 3142, pp. 581–592. Springer, Heidelberg (2004)

    Google Scholar 

  12. Golumbic, M.C., Lewenstein, M.: New results on induced matchings. Discrete Applied Mathematics 101(1-3), 157–165 (2000)

    Article  MATH  Google Scholar 

  13. Gotthilf, Z., Lewenstein, M.: Tighter approximations for maximum induced matchings in regular graphs. In: Erlebach, T., Persinao, G. (eds.) WAOA 2005. LNCS, vol. 3879, pp. 270–281. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  14. Guo, J., Niedermeier, R.: Invitation to data reduction and problem kernelization. SIGACT News 38(1), 31–45 (2007)

    Article  Google Scholar 

  15. Guo, J., Niedermeier, R.: Linear problem kernels for NP-hard problems on planar graphs. In: Arge, L., Cachin, C., Jurdzinski, T., Tarlecki, A. (eds.) ICALP 2007. LNCS, vol. 4596, pp. 375–386. Springer, Heidelberg (2007)

    Google Scholar 

  16. Guo, J., Niedermeier, R., Wernicke, S.: Fixed-parameter tractability results for full-degree spanning tree and its dual. In: Bodlaender, H.L., Langston, M.A. (eds.) IWPEC 2006. LNCS, vol. 4169, pp. 203–214. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  17. Ko, C.W., Shepherd, F.B.: Bipartite domination and simultaneous matroid covers. SIAM Journal on Discrete Mathematics 16(4), 517–523 (2003)

    Article  MATH  Google Scholar 

  18. Kobler, D., Rotics, U.: Finding maximum induced matchings in subclasses of claw-free and P 5-free graphs, and in graphs with matching and induced matching of equal maximum size. Algorithmica 37(4), 327–346 (2003)

    Article  MATH  Google Scholar 

  19. Lozin, V.V., Rautenbach, D.: Some results on graphs without long induced paths. Information Processing Letters 88(4), 167–171 (2003)

    Article  Google Scholar 

  20. Moser, H., Thilikos, D.M.: Parameterized complexity of finding regular induced subgraphs. In: Proceedings of ACiD 2006. Texts in Algorithmics, vol. 7, pp. 107–118. College Publications (2006)

    Google Scholar 

  21. Niedermeier, R.: Invitation to Fixed-Parameter Algorithms. Oxford University Press, Oxford (2006)

    MATH  Google Scholar 

  22. Stockmeyer, L.J., Vazirani, V.V.: NP-completeness of some generalizations of the maximum matching problem. Information Processing Letters 15(1), 14–19 (1982)

    Article  MATH  Google Scholar 

  23. Zito, M.: Induced matchings in regular graphs and trees. In: Widmayer, P., Neyer, G., Eidenbenz, S. (eds.) WG 1999. LNCS, vol. 1665, pp. 89–100. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut für Informatik, Friedrich-Schiller-Universität Jena, Ernst-Abbe-Platz 2, D-07743 Jena, Germany

    Hannes Moser

  2. The Institute of Mathematical Sciences, C.I.T Campus, Taramani, Chennai 600113, India

    Somnath Sikdar

Authors
  1. Hannes Moser
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Somnath Sikdar
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Franco P. Preparata Qizhi Fang

Rights and permissions

Reprints and permissions

Copyright information

© 2007 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Moser, H., Sikdar, S. (2007). The Parameterized Complexity of the Induced Matching Problem in Planar Graphs. In: Preparata, F.P., Fang, Q. (eds) Frontiers in Algorithmics. FAW 2007. Lecture Notes in Computer Science, vol 4613. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73814-5_32

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-73814-5_32

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-73813-8

  • Online ISBN: 978-3-540-73814-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation