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Exact Computation of Maximum Induced Forest

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Algorithm Theory – SWAT 2006 (SWAT 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4059))

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Abstract

We propose a backtrack algorithm that solves a generalized version of the Maximum Induced Forest problem (MIF) in time O *(1.8899n). The MIF problem is complementary to finding a minimum Feedback Vertex Set (FVS), a well-known intractable problem. Therefore the proposed algorithm can find a minimum FVS as well. To the best of our knowledge, this is the first algorithm that breaks the O *(2n) barrier for the general case of FVS. Doing the analysis, we apply a more sophisticated measure of the problem size than the number of nodes of the underlying graph.

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References

  1. Byskov, J.: Enumerating maximal independent sets with applications to graph colouring. Operations Research Letters 32(6), 547–556 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  2. Dantsin, E., Goerdt, A., Hirsch, E., Kannan, R., Kleinberg, J., Papadimitriou, C., Raghavan, P., Schöning, U.: A deterministic (2-2/(k+1))n algorithm for k-sat based on local search. Theor. Comput. Sci. 289(1), 69–83 (2002)

    Article  MATH  Google Scholar 

  3. Eppstein, D.: Improved algorithms for 3-coloring, 3-edge coloring and constraint satisfaction. In: SODA 2001, pp. 329–337 (2001)

    Google Scholar 

  4. Fomin, F., Grandoni, F., Kratsch, D.: Measure and conquer: Domination - a case study. In: Caires, L., Italiano, G.F., Monteiro, L., Palamidessi, C., Yung, M. (eds.) ICALP 2005. LNCS, vol. 3580, pp. 191–203. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  5. Fomin, F., Grandoni, F., Kratsch, D.: Some new techniques in design and analysis of exact (exponential) algorithms. Bulletin of the EATCS 87, 47–77 (2005)

    MATH  MathSciNet  Google Scholar 

  6. Fomin, F., Pyatkin, A.: Finding minimum feedback vertex set in bipartite graphs. Report N 291, Department of Informatics, University of Bergen (2005)

    Google Scholar 

  7. Karp, R.: Reducibility among combinatorial problems. In: Complexity of Computer Computations (1972)

    Google Scholar 

  8. Raman, V., Saurabh, S., Sikdar, S.: Improved Exact Exponential Algorithms for Vertex Bipartization and Other Problems. In: Coppo, M., Lodi, E., Pinna, G.M. (eds.) ICTCS 2005. LNCS, vol. 3701, pp. 375–389. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  9. Robson, J.: Algorithms for maximum independent sets. Journal of Algorithms 7, 425–440 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  10. Woeginger, G.: Exact algorithms for NP-hard problems: A survey. In: Jünger, M., Reinelt, G., Rinaldi, G. (eds.) Combinatorial Optimization - Eureka, You Shrink! LNCS, vol. 2570, pp. 185–207. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

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Author information

Authors and Affiliations

  1. Computer Science Department, University College Cork, Ireland

    Igor Razgon

Authors
  1. Igor Razgon
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Editors and Affiliations

  1. MADALGO, Department of Computer Science, University of Aarhus, Denmark

    Lars Arge

  2. Institute of Mathematics and Computer Science, University of Latvia, Raiņa bulvāris 29, Rīga, LV-1459, Latvia

    Rusins Freivalds

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© 2006 Springer-Verlag Berlin Heidelberg

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Razgon, I. (2006). Exact Computation of Maximum Induced Forest. In: Arge, L., Freivalds, R. (eds) Algorithm Theory – SWAT 2006. SWAT 2006. Lecture Notes in Computer Science, vol 4059. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11785293_17

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  • DOI: https://doi.org/10.1007/11785293_17

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-35753-7

  • Online ISBN: 978-3-540-35755-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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