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Minimum Maximal Acyclic Matching in Proper Interval Graphs

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Algorithms and Discrete Applied Mathematics (CALDAM 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13947))

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Abstract

Given a graph G, Min-Max-Acy-Matching is the problem of finding a maximal matching M in G of minimum cardinality such that the set of M-saturated vertices induces an acyclic subgraph in G. The decision version of Min-Max-Acy-Matching is known to be \(\textsf{NP}\)-complete even for planar perfect elimination bipartite graphs. In this paper, we give the first positive algorithmic result for Min-Max-Acy-Matching by presenting a linear-time algorithm for computing a minimum cardinality maximal acyclic matching in proper interval graphs.

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Notes

  1. 1.

    Let \(K_{n}\) and \(P_{n}\) denote a complete graph and a path graph on n vertices, respectively.

References

  1. Bazgan, C., et al.: The many facets of upper domination. Theor. Comput. Sci. 717, 2–25 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  2. Boria, N., Croce, F.D., Paschos, V.T.: On the max min vertex cover problem. Discret. Appl. Math. 196, 62–71 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  3. Chaudhary, J., Mishra, S., Panda, B.S.: On the complexity of minimum maximal acyclic matching. In: Proceedings of the 28th International Computing and Combinatorics Conference (COCOON) (to appear)

    Google Scholar 

  4. Chaudhary, J., Panda, B.S.: On the complexity of minimum maximal uniquely restricted matching. Theor. Comput. Sci. 882, 15–28 (2021)

    Article  MathSciNet  MATH  Google Scholar 

  5. Damaschke, P.: Parameterized algorithms for double hypergraph dualization with rank limitation and maximum minimal vertex cover. Discret. Optim. 8(1), 18–24 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  6. Dublois, L., Hanaka, T., Ghadikolaei, M.K., Lampis, M., Melissinos, N.: (In)approximability of maximum minimal FVS. In: Proceedings of the 31st International Symposium on Algorithms and Computation (ISAAC), Leibniz International Proceedings in Informatics, vol. 181, pp. 3:1–14 (2020)

    Google Scholar 

  7. Goddard, W., Hedetniemi, S.M., Hedetniemi, S.T., Laskar, R.: Generalized subgraph-restricted matchings in graphs. Discret. Math. 293(1–3), 129–138 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  8. Jamison, R.E., Laskar, R.: Elimination orderings of chordal graphs. In: Proceedings of the Seminar on Combinatorics and Applications, pp. 192–200 (1982)

    Google Scholar 

  9. Lepin, V.V.: A linear algorithm for computing of a minimum weight maximal induced matching in an edge-weighted tree. Electron. Notes Discret. Math. 24, 111–116 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  10. Orlovich, Y.L., Finke, G., Gordon, V., Zverovich, I.: Approximability results for the maximum and minimum maximal induced matching problems. Discret. Optim. 5(3), 584–593 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  11. Orlovich, Y. L., Zverovich, I. E.: Maximal induced matchings of minimum/ maximum size. Technical report, DIMACS TR 2004–26 (2004)

    Google Scholar 

  12. Panda, B.S., Chaudhary, J.: Acyclic matching in some subclasses of graphs. In: Gasieniec, L., Klasing, R., Radzik, T. (eds.) IWOCA 2020. LNCS, vol. 12126, pp. 409–421. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48966-3_31

    Chapter  Google Scholar 

  13. Panda, B.S., Das, S.K.: A linear time recognition algorithm for proper interval graphs. Inf. Process. Lett. 87(3), 153–161 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  14. Panda, B.S., Pandey, A.: On the complexity of minimum cardinality maximal uniquely restricted matching in graphs. In: Arumugam, S., Bagga, J., Beineke, L.W., Panda, B.S. (eds.) ICTCSDM 2016. LNCS, vol. 10398, pp. 218–227. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-64419-6_29

    Chapter  Google Scholar 

  15. Yannakakis, M., Gavril, F.: Edge dominating sets in graphs. SIAM J. Appl. Math. 38(3), 364–372 (1980)

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Computer Science, Ben-Gurion University of the Negev, Beersheba, Israel

    Juhi Chaudhary

  2. Department of Mathematics, Indian Institute of Technology Madras, Chennai, India

    Sounaka Mishra

  3. Department of Mathematics, Indian Institute of Technology Delhi, New Delhi, India

    B. S. Panda

Authors
  1. Juhi Chaudhary
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  2. Sounaka Mishra
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  3. B. S. Panda
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Corresponding author

Correspondence to Juhi Chaudhary .

Editor information

Editors and Affiliations

  1. Department of Computer Science and Engineering, Indian Institute of Technology Delhi, New Delhi, India

    Amitabha Bagchi

  2. Dhirubhai Ambani Institute of Information and Communication Technology, Gandhinagar, India

    Rahul Muthu

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Chaudhary, J., Mishra, S., Panda, B.S. (2023). Minimum Maximal Acyclic Matching in Proper Interval Graphs. In: Bagchi, A., Muthu, R. (eds) Algorithms and Discrete Applied Mathematics. CALDAM 2023. Lecture Notes in Computer Science, vol 13947. Springer, Cham. https://doi.org/10.1007/978-3-031-25211-2_29

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  • DOI: https://doi.org/10.1007/978-3-031-25211-2_29

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-25210-5

  • Online ISBN: 978-3-031-25211-2

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