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International Conference on Current Trends in Theory and Practice of Computer Science

SOFSEM 1998: SOFSEM’ 98: Theory and Practice of Informatics pp 168–185Cite as

Some Prospects forEfficient Fixed Parameter Algorithms

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1521))

Abstract

Recent time has seen quite some progress in the development of exponential time algorithms for NP-hard problems, where the base of the exponential term is fairly small. These developments are also tightly related to the theory of fixed parameter tractability. In this incomplete survey, we explain some basic techniques in the design of efficient fixed parameter algorithms, discuss deficiencies of parameterized complexity theory, and try to point out some future research challenges. The focus of this paper is on the design of efficient algorithms and not on a structural theory of parameterized complexity. Moreover, our emphasis will be laid on two exemplifying issues: Vertex Cover and MaxSat problems.

Supported by a Feodor Lynen fellowship of the Alexander von Humboldt-Stiftung, Bonn, and the Center for Discrete Mathematics, Theoretical Computer Science and Applications (DIMATIA), Prague. Author’s address in 1998: DIMATIA MFF UK, Charles University, Malostranské námĚstí 25, 118 00 Praha 1, Czech Republic.

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References

  1. K. A. Abrahamson, R. G. Downey, and M. R. Fellows. Fixed-parameter tractability and completeness IV: On completeness for W[P] and PSPACE analogues. Annals of Pure and Applied Logic, 73:235–276, 1995.

    Article  MATH  MathSciNet  Google Scholar 

  2. N. Alon, R. Yuster, and U. Zwick. Color-coding. J. ACM, 42(4):844–856, 1995.

    Article  MATH  MathSciNet  Google Scholar 

  3. S. Arnborg, D. G. Corneil, and A. Proskurowski. Complexity of finding embeddings in a k-tree. SIAM J. Alg. Disc. Meth., 8:277–284, 1987.

    Article  MATH  MathSciNet  Google Scholar 

  4. S. Arora, C. Lund, R. Motwani, M. Sudan, and M. Szegedy. Proof verification and hardness of approximation problems. In Proceedings of the 33d IEEE Conference on Foundations of Computer Science, pages 14–23, 1992.

    Google Scholar 

  5. R. Balasubramanian, M. R. Fellows, and V. Raman. An improved fixed parameter algorithm for vertex cover. Information Processing Letters, 65(3):163–168, 1998.

    Article  MathSciNet  Google Scholar 

  6. R. Battiti and M. Protasi. Reactive Search, a history-base heuristic for MAX-SAT. ACM Journal of Experimental Algorithmics, 2:Article 2, 1997.

    Google Scholar 

  7. A. Blummer, A. Ehrenfeucht, D. Haussler, and M. K. Warmuth. Learnability and the Vapnik-Chervonenkis dimension. J. ACM, 36:929–965, 1989.

    Article  Google Scholar 

  8. H. L. Bodlaender. A linear time algorithm for finding tree-decompositions of small treewidth. SIAM J. Comput., 25:1305–1317, 1996.

    Article  MATH  MathSciNet  Google Scholar 

  9. R. B. Boppana and M. Sipser. The complexity of finite functions. In J. van Leeuwen, editor, Algorithms and Complexity, volume A of Handbook of Theoretical Computer Science, chapter 14, pages 757–804. Elsevier, 1990.

    Google Scholar 

  10. J. F. Buss and J. Goldsmith. Nondeterminism within P. SIAM J. Comput., 22(3):560–572, 1993.

    Article  MATH  MathSciNet  Google Scholar 

  11. L. Cai and J. Chen. On fixed-parameter tractability and approximability of NP optimization problems. J. Comput. Syst. Sci., 54:465–474, 1997.

    Article  MATH  MathSciNet  Google Scholar 

  12. D. Coppersmith and S. Winograd. Matrix multiplication via arithmetical progression. J. Symbolic Computations, 9:251–280, 1990.

    Article  MATH  MathSciNet  Google Scholar 

  13. T. H. Cormen, C. E. Leiserson, and R. L. Rivest. Introduction to Algorithms. The MIT Press, 1990.

    Google Scholar 

  14. P. Crescenzi and V. Kann. A compendium of NP optimization problems. Available as http://www.nada.kth.se/theory/problemlist.html, Apr. 1997.

  15. E. Dantsin, M. Gavrilovich, E. A. Hirsch, and B. Konev. Approximation algorithms for Max SAT: a better performance ratio at the cost of a longer running time. Technical Report PDMI preprint 14/1998, Steklov Institute of Mathematics at St. Petersburg, 1998.

    Google Scholar 

  16. R. G. Downey, P. Evans, and M. R. Fellows. Parameterized learning complexity. In 6th Annual Conference on Learning Theory, COLT’93, pages 51–57. ACM Press, 1993.

    Google Scholar 

  17. R. G. Downey and M. R. Fellows. Fixed parameter tractability and completeness III. In Complexity Theory: Current Research, Edited by K. Ambos-Spies, S. Homer, and U. Schöning, Cambridge University Press, pages 191–225. 1993.

    Google Scholar 

  18. R. G. Downey and M. R. Fellows. Fixed-parameter tractability and completeness I: Basic results. SIAM Journal on Computing, 24(4):873–921, August 1995.

    Google Scholar 

  19. R. G. Downey and M. R. Fellows. Fixed-parameter tractability and completeness II: On completeness for W[1]. Theoretical Computer Science, 141:109–131, 1995.

    Article  MATH  MathSciNet  Google Scholar 

  20. R. G. Downey and M. R. Fellows. Parameterized computational feasibility. In P. Clote, J. Remmel (eds.): Feasible Mathematics II, pages 219–244. Boston: BirkhÄuser, 1995.

    Google Scholar 

  21. R. G. Downey and M. R. Fellows. Parameterized Complexity. Springer-Verlag, 1998.

    Google Scholar 

  22. R. G. Downey, M. R. Fellows, and U. Stege. Parameterized complexity: A framework for systematically confronting computational intractability. In F. Roberts, J. Kratochvíl, and J. NešetŘil, editors, The Future of Discrete Mathematics: Proceedings of the First DIM ATIA Symposium, June 1997, AMS-DIMACS Proceedings Series. AMS, 1998. To appear. Available through http://www.inf.ethz.ch/personal/stege.

  23. R.C. Evans. Testing repairable RAMs and mostly good memories. In Proceedings of the IEEE Int. Test Conf., pages 49–55, 1981.

    Google Scholar 

  24. U. Feige and M. X. Goemans. Approximating the value of two prover proof systems, with applications to MAX 2SAT and MAX DICUT. In 3d IEEE Israel Symposium on the Theory of Computing and Systems, pages 182–189, 1995.

    Google Scholar 

  25. M. R. Fellows and M. A. Langston. Nonconstructive advances in polynomial-time complexity. Information Processing Letters, 26:157–162, 1987.

    Article  MATH  MathSciNet  Google Scholar 

  26. H. Fernau and R. Niedermeier. Efficient algorithms for constraint bipartite vertex cover problems. Manuscript, July 1998.

    Google Scholar 

  27. M. Garey and D. Johnson. Computers and Intractability: A Guide to the Theory of NP-completeness. Freeman, San Francisco, 1979.

    MATH  Google Scholar 

  28. M. X. Goemans and D. P. Williamson. Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming. J. ACM, 42:1115–1145, 1995.

    Article  MATH  MathSciNet  Google Scholar 

  29. P. Hansen and B. Jaumard. Algorithms for the maximum satisfiability problem. Computing, 44:279–303, 1990.

    Article  MATH  MathSciNet  Google Scholar 

  30. N. Hasan and C. L. Liu. Minimum fault coverage in reconfigurable arrays. In 18th Int. Symp. on Fault-Tolerant Computing Systems (FTCS’88), pages 348–353. IEEE Computer Society Press, 1988.

    Google Scholar 

  31. N. Hasan and C. L. Liu. Fault covers in reconfigurable PLAs. In 20th Int. Symp. on Fault-Tolerant Computing Systems (FTCS’90), pages 166–173. IEEE Computer Society Press, 1990.

    Google Scholar 

  32. J. Hastad. Some optimal inapproximability results.In proceedings of the 29th ACM Symposium on Theory of Computing, pages 1–10, 1997.

    Google Scholar 

  33. D. S. Hochbaum, editor. Approximation algorithms for NP-hard problems. Boston, MA: PWS Publishing Company, 1997.

    Google Scholar 

  34. D.S Johnson. Approximation algorithms for combinatorial problems. J. Comput. Syst. Sci., 9:256–278, 1974.

    Article  MATH  Google Scholar 

  35. J. H. Kim and S. M. Reddy. On the design of fault-tolerant two-dimensional systolic arrays for yield enhancement. IEEE Transactions on Computers, 38(4):515–525, Apr. 1989.

    Google Scholar 

  36. P. G. Kolaitis and M. N. Thakur. Approximation properties of NP minimization classes. J. Comput. Syst. Sci., 50:391–411, 1995.

    Article  MATH  MathSciNet  Google Scholar 

  37. S.-Y. Kuo and I.-Y. Chen. Efficient reconfiguration algorithms for degradable VLSI/WSI arrays. IEEE Transactions on Computer-Aided Design, 11(10):1289–1300 1300, 1992.

    Article  Google Scholar 

  38. S.-Y. Kuo and W. Fuchs. Efficient spare allocation for reconfigurable arrays. IEEE Design and Test, 4:24–31, Feb. 1987.

    Google Scholar 

  39. C. P. Low and H. W. Leong. A new class of efficient algorithms for reconfiguration of memory arrays. IEEE Transactions on Computers, 45(5):614–618, 1996.

    Article  MATH  Google Scholar 

  40. M. Mahajan and V. Raman. Parametrizing above guaranteed values: MaxSat and MaxCut. Technical Report TR97-033, ECCC Trier, 1997. To appear in Journal of Algorithms.

    Google Scholar 

  41. K. Mehlhorn. Graph algorithms and NP-completeness. Heidelberg: Springer, 1984.

    MATH  Google Scholar 

  42. J. NešetŘil and S. Poljak. On the complexity of the subgraph problem. Commentationes Mathematicae Universitatis Carolinae, 26(2):415–419, 1985.

    MATH  MathSciNet  Google Scholar 

  43. R. Niedermeier and P. Rossmanith. New upper bounds for MaxSat. Technical Report KAM-DIMATIA Series 98–401, Faculty of Mathematics and Physics, Charles University, Prague, July 1998. Submitted for publication.

    Google Scholar 

  44. C.H. Papadimitriou. Computational Complexity. Addison-Wesley, 1994.

    Google Scholar 

  45. C. H. Papadimitriou and M. Yannakakis. Optimization, approximation, and complexity classes. J. Comput. Syst. Sci., 43:425–440, 1991.

    Article  MATH  MathSciNet  Google Scholar 

  46. C. H. Papadimitriou and M. Yannakakis. On limited nondeterminism and the complexity of the V-C dimension. J. Comput. Syst. Sci., 53:161–170, 1996.

    Article  MATH  MathSciNet  Google Scholar 

  47. V. Raman. Parameterized complexity. In Proceedings of the 7th National Seminar on Theoretical Computer Science (Chennai, India), pages I-1–I-18, June 1997.

    Google Scholar 

  48. N. Robertson and P. D. Seymour. Graph minors⊕-survey. In I. Anderson, editor Surveys in Combinatorics, pages 153–171. Cambridge University Press, 1985.

    Google Scholar 

  49. M. D. Smith and P. Mazumder. Generation of minimal vertex covers for row/column allocation in self-repairable arrays. IEEE Transactions on Computers, 45(1):109–115, 1996.

    Article  MATH  Google Scholar 

  50. J. A. Telle and A. Proskurowski. Algorithms for vertex partitioning problems on partial k-trees. SIAM Journal on Discrete Mathematics, 10(4):529–550, 1997.

    Article  MATH  MathSciNet  Google Scholar 

  51. L. Trevisan, G. Sorkin, M. Sudan, and D. P. Williamson. Gadgets, approximation, and linear programming. In Proceedings of the 37th IEEE Conference on Foundations of Computer Science, pages 617–626, 1996.

    Google Scholar 

  52. L. Youngs and S. Paramanandam. Mapping and repairing embedded-memory defects. IEEE Design and Test, 14(1):18–24, 1997.

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Wilhelm-Schickard-Institut für Informatik, UniversitÄt Tübingen, Sand 13, D-72076, Tübingen, Fed. Rep. of Germany

    Rolf Niedermeier

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  1. Rolf Niedermeier
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  1. Department of Computer Science, Comenius University, SK-84215, Bratislava, Slovakia

    Branislav Rovan

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Niedermeier, R. (1998). Some Prospects forEfficient Fixed Parameter Algorithms. In: Rovan, B. (eds) SOFSEM’ 98: Theory and Practice of Informatics. SOFSEM 1998. Lecture Notes in Computer Science, vol 1521. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-49477-4_12

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  • DOI: https://doi.org/10.1007/3-540-49477-4_12

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