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Efficient Approximation of Combinatorial Problems by Moderately Exponential Algorithms

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Algorithms and Data Structures (WADS 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5664))

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Abstract

We design approximation algorithms for several NP-hard combinatorial problems achieving ratios that cannot be achieved in polynomial time (unless a very unlikely complexity conjecture is confirmed) with worst-case complexity much lower (though super-polynomial) than that of an exact computation. We study in particular max independent set, min vertex cover and min set cover and then extend our results to max clique, max bipartite subgraph and max set packing.

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References

  1. Woeginger, G.J.: 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 

  2. Ausiello, G., Crescenzi, P., Gambosi, G., Kann, V., Marchetti-Spaccamela, A., Protasi, M.: Complexity and approximation. In: Combinatorial optimization problems and their approximability properties. Springer, Berlin (1999)

    Google Scholar 

  3. Hochbaum, D.S. (ed.): Approximation algorithms for NP-hard problems. PWS, Boston (1997)

    MATH  Google Scholar 

  4. Vazirani, V.: Approximation algorithms. Springer, Berlin (2001)

    MATH  Google Scholar 

  5. Arora, S., Lund, C., Motwani, R., Sudan, M., Szegedy, M.: Proof verification and intractability of approximation problems. J. Assoc. Comput. Mach. 45, 501–555 (1998)

    Article  MATH  Google Scholar 

  6. Zuckerman, D.: Linear degree extractors and the inapproximability of max clique and chromatic number. In: Proc. STOC 2006, pp. 681–690 (2006)

    Google Scholar 

  7. Björklund, A., Husfeldt, T.: Inclusion-exclusion algorithms for counting set partitions. In: Proc. FOCS 2006, pp. 575–582 (2006)

    Google Scholar 

  8. Cygan, M., Kowalik, L., Pilipczuk, M., Wykurz, M.: Exponential-time approximation of hard problems. arXiv:0810.4934v1 (2008), http://arxiv.org/abs/0810.4934v1

  9. Cai, L., Huang, X.: Fixed-parameter approximation: conceptual framework and approximability results. In: Bodlaender, H.L., Langston, M.A. (eds.) IWPEC 2006. LNCS, vol. 4169, pp. 96–108. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  10. Chen, Y., Grohe, M., Grüber, M.: On parameterized approximability. In: Bodlaender, H.L., Langston, M.A. (eds.) IWPEC 2006. LNCS, vol. 4169, pp. 109–120. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  11. Downey, R.G., Fellows, M.R., McCartin, C.: Parameterized approximation problems. In: Bodlaender, H.L., Langston, M.A. (eds.) IWPEC 2006. LNCS, vol. 4169, pp. 121–129. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  12. Vassilevska, V., Williams, R., Woo, S.: Confronting hardness using a hybrid approach. In: Proc. Symposium on Discrete Algorithms, SODA 2006, pp. 1–10 (2006)

    Google Scholar 

  13. Bourgeois, N., Escoffier, B., Paschos, V.T.: Efficient approximation by “low-complexity” exponential algorithms. Cahier du LAMSADE 271, LAMSADE, Université Paris-Dauphine (2007), http://www.lamsade.dauphine.fr/cahiers/PDF/cahierLamsade271.pdf

  14. Bourgeois, N., Escoffier, B., Paschos, V.T.: Efficient approximation of min set cover by “low-complexity” exponential algorithms. Cahier du LAMSADE 278, LAMSADE, Université Paris-Dauphine (2008), http://www.lamsade.dauphine.fr/cahiers/PDF/cahierLamsade278.pdf

  15. Robson, J.M.: Finding a maximum independent set in time O(2n/4). Technical Report 1251-01, LaBRI, Université de Bordeaux I (2001)

    Google Scholar 

  16. Khot, S., Regev, O.: Vertex cover might be hard to approximate to within 2 − ε. In: Proc. Annual Conference on Computational Complexity, CCC 2003, pp. 379–386 (2003)

    Google Scholar 

  17. Chen, J., Kanj, I., Jia, W.: Vertex cover: further observations and further improvements. J. Algorithms 41, 280–301 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  18. Nemhauser, G.L., Trotter, L.E.: Vertex packings: structural properties and algorithms. Math. Programming 8, 232–248 (1975)

    Article  MathSciNet  MATH  Google Scholar 

  19. Berman, P., Fujito, T.: On the approximation properties of independent set problem in degree 3 graphs. In: Sack, J.-R., Akl, S.G., Dehne, F., Santoro, N. (eds.) WADS 1995. LNCS, vol. 955, pp. 449–460. Springer, Heidelberg (1995)

    Chapter  Google Scholar 

  20. Duh, R., Fürer, M.: Approximation of k-set cover by semi-local optimization. In: Proc. STOC 1997, pp. 256–265 (1997)

    Google Scholar 

  21. van Rooij, J., Bodlaender, H.: Design by measure and conquer, a faster exact algorithm for dominating set. In: Albers, S., Weil, P. (eds.) Proc. International Symposium on Theoretical Aspects of Computer Science, STACS 2008, pp. 657–668 (2008)

    Google Scholar 

  22. Björklund, A., Husfeldt, T., Koivisto, M.: Set partitioning via inclusion-exclusion. SIAM J. Comput. (To appear in the special issue dedicated to selected papers from FOCS 2006)

    Google Scholar 

  23. Simon, H.U.: On approximate solutions for combinatorial optimization problems. SIAM J. Disc. Math. 3, 294–310 (1990)

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. LAMSADE, CNRS FRE 3234 and Université Paris-Dauphine, France

    Nicolas Bourgeois, Bruno Escoffier & Vangelis Th. Paschos

Authors
  1. Nicolas Bourgeois
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  2. Bruno Escoffier
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  3. Vangelis Th. Paschos
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Editor information

Editors and Affiliations

  1. Carleton University, Ottawa, Canada

    Frank Dehne

  2. Department of Computer Science, University of Calgary, 2500 University Drive N.W., T2N 1N4, Calgary, AB, Canada

    Marina Gavrilova

  3. School of Computer Science, Carleton University, 1125 Colonel By Drive, Ottawa, P.O. Box, K1S 5B6, Ontario, Canada

    Jörg-Rüdiger Sack

  4. University of Calgary, Calgary, AB, Canada

    Csaba D. Tóth

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Bourgeois, N., Escoffier, B., Paschos, V.T. (2009). Efficient Approximation of Combinatorial Problems by Moderately Exponential Algorithms. In: Dehne, F., Gavrilova, M., Sack, JR., Tóth , C.D. (eds) Algorithms and Data Structures. WADS 2009. Lecture Notes in Computer Science, vol 5664. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03367-4_44

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  • DOI: https://doi.org/10.1007/978-3-642-03367-4_44

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-03366-7

  • Online ISBN: 978-3-642-03367-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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