Skip to main content
SpringerLink
Log in

Towards a Predictive Computational Complexity Theory

  • Conference paper
  • First Online:
Automata, Languages and Programming (ICALP 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2380))

Included in the following conference series:

Abstract

Over the last three decades, language recognition models of computation and associated resource bounded reductions have played a central role in characterizing the computational complexity of combinatorial problems. However, due to their generality, these concepts have inherent limitations - they typically ignore the underlying structure and semantics of the problem instances. Thus they are generally not “robust” in terms of simultaneously classifying variants of the original problem.

Work supported by the Department of Energy under Contract W-7405-ENG-36.

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 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
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. S. Agarwal and A. Condon. On approximation algorithms for hierarchical MAX-SAT. J. of Algorithms, 26, 1998, pp. 141–165.

    Article  MATH  MathSciNet  Google Scholar 

  2. E. Amaldi and V. Kann. The complexity and approximability of finding maximum feasible subsystems of linear relations. Theoretical Computer Science (TCS) 147, pp. 181–210, 1995.

    Article  MATH  MathSciNet  Google Scholar 

  3. S. Arnborg, B. Courcelle, A. Proskurowski and D. Seese. An algebraic theory of graph reduction. J. of the ACM (JACM), 40, 1993, pp. 1134–1164.

    Article  MATH  MathSciNet  Google Scholar 

  4. S. Arora, C. Lund, R. Motwani, M. Sudan and M. Szegedy. Proof verification and hardness of approximation problems. J.of the ACM (JACM), 45, 1998, pp. 501–555.

    Article  MATH  MathSciNet  Google Scholar 

  5. S. Arora. Polynomial time approximation scheme for Euclidean TSP and other geometric problems. J.of the ACM (JACM), 45(5), pp. 753–682, 1998.

    Article  MATH  MathSciNet  Google Scholar 

  6. G. Ausiello, P. Crescenzi, G. Gambosi, V. Kann, A. Marchetti-Spaccamela and M. Protasi. Complexity and approximation: Combinatorial optimization problems and their approximability properties, Springer Verlag, 1999.

    Google Scholar 

  7. B. S. Baker. “Approximation algorithms for NP-complete problems on planar graphs”, J. of the ACM (JACM), Vol. 41, No. 1, Jan. 1994, pp. 153–180.

    Article  MATH  Google Scholar 

  8. R. Beigel, W. Gasarch. “On the complexity of finding the chromatic number of recursive graphs,” Parts I and II, Annals of Pure and Applied Logic, 45, 1989, pp. 1–38 and 227–247.

    Article  MATH  MathSciNet  Google Scholar 

  9. J.L. Bentley, T. Ottmann, and P. Widmayer. The complexity of manipulating hierarchically defined sets of intervals. Advances in Computing Research 1, F.P. Preparata (ed.), 1983, pp. 127–158.

    Google Scholar 

  10. U. Bertele and F. Brioschi. Nonserial Dynamic Programming, Academic Press, NY, 1972.

    MATH  Google Scholar 

  11. H. Bodlaender Dynamic programming on graphs of bounded treewidth. Proc. 15th International Colloquium on Automata Languages and Programming (ICALP), LNCS Vol. 317, 1988, pp. 105–118.

    Google Scholar 

  12. A. Condon, J. Feigenbaum, C. Lund and P. Shor. Probabilistically checkable debate systems and approximation algorithms for PSPACE-Hard Functions. Chicago Journal of Theoretical Computer Science, Vol. 1995, No. 4. http://www.cs.uchicago.edu/publications/cjtcs/articles/1995/4/ contents.html.

  13. A. Condon, J. Feigenbaum, C. Lund and P. Shor. Random debaters and the hardness of approximating stochastic functions. SIAM J. Computing, 26, 1997, pp. 369–400.

    Article  MATH  MathSciNet  Google Scholar 

  14. N. Creignou. A dichotomy theorem for maximum generalized satisfiability problems. J. of Computer and System Sciences (JCSS), 51, 1995, pp. 511–522.

    Article  MathSciNet  Google Scholar 

  15. N. Creignou and M. Hermann. Complexity of generalized satisfiability counting problems. Information and Computation 125(1), pp. 1–12, 1996.

    Article  MATH  MathSciNet  Google Scholar 

  16. N. Creignou, S. Khanna, and M. Sudan Complexity classifications of Boolean constraint satisfaction problems SIAM Monographs on Discrete Mathematics and Applications 7, 2001.

    Google Scholar 

  17. N. Creignou, S. Khanna, and M. Sudan. Complexity classifications of Boolean constraint satisfaction problems. SIG ACT News, Volume 32,4(121), Complexity Theory Column 34, pp. 24–33, November 2001.

    Google Scholar 

  18. V. Dalmau. Computational complexity of problems over generalized formulas. Ph.D. thesis, Dept. of Computer Science, U. Politecnica De Catalunya.

    Google Scholar 

  19. R. Downey and M. Fellows. Parameterized Complexity, Springer Verlag, 1998.

    Google Scholar 

  20. D. Eppstein “Subgraph Isomorphism in planar graphs and related problems,” 6th ACM-SIAM Symposium on Discrete Algorithms (SODA), 1995, pp. 632–640.

    Google Scholar 

  21. A. Ehrenfeucht, J. Engelfriet and G. Rosenberg. Finite Languages for Representation of Finite Graphs. J. Computer and System Sciences (JCSS), (52), pp. 170–184, 1996.

    Google Scholar 

  22. T. Erlebach, K. Jansen and E. Seidel. Polynomial time approximation schemes for geometric Graphs. Proc. 12th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), 2001, pp. 671–679.

    Google Scholar 

  23. T. Feder and M. Vardi. The computational structure of monotone monadic SNP and constraint satisfaction: A study through datalog and group Theory. SIAM J. Computing, 28(1): 57–104 (1998).

    Article  MATH  MathSciNet  Google Scholar 

  24. J. Feigenbaum. “Games, complexity classes and approximation algorithms,” invited talk at the International Congress on Mathematics, Berlin, 1998.

    Google Scholar 

  25. A. Fraenkel and Y. Yesha. Complexity of problems in games, graphs, and algebraic equations. Discrete Mathematics, 1, 1979, pp. 15–30.

    Article  MATH  MathSciNet  Google Scholar 

  26. M. Freedman. k-SAT on groups and Undecidability. Proc. 30th ACM Annual Symposium on Theory of Computing (STOC). 1998, pp. 572–576.

    Google Scholar 

  27. M. Freedman. Limits, logic and computation. Proc. National Academy of Sciences, USA, 95, 1998, pp. 95–97.

    Article  MATH  Google Scholar 

  28. M. Garey and D. Johnson. Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman, San Francisco, 1979.

    MATH  Google Scholar 

  29. M. Grohe. Local tree-width, excluded minors, and approximation algorithms. To appear in Combinatorica, 2002.

    Google Scholar 

  30. M. Grohe and M. Frick. Deciding first-order properties of locally tree-decomposable structures. To appear in J. of the ACM (JACM). Conference version appeared in Proc. 26th International Colloquium on Automata, Languages, and Programming, Lecture Notes in Computer Science 1644, Springer-Verlag, 1999.

    Google Scholar 

  31. T. Hirst and D. Harel. “Taking it to the Limit: On infinite variants of NP-complete problems,” Proc. 8th IEEE Annual Conference on Structure in Complexity Theory, 1993, pp. 292–304.

    Google Scholar 

  32. D. S. Hochbaum and W. Maass. Approximation schemes for covering and packing problems in image processing and VLSI. J. of the ACM (JACM), 32(1), pp. 130–136, 1985.

    Article  MATH  MathSciNet  Google Scholar 

  33. D. Hochbaum(Ed.). Approximation Algorithms for NP-Hard Problems. PWS Publishing Company, Boston, MA, 1997.

    Google Scholar 

  34. F. Höfting, T. Lengauer, and E. Wanke. Processing of hierarchically defined graphs and graph families. Data Structures and Efficient Algorithms (Final Report on the DFG Special Joint Initiative), Springer-Verlag, LNCS 594, 1992, pp. 44–69.

    Google Scholar 

  35. H. Hunt III, R. Stearns and M. Marathe. Generalized CNF satisfiability problems and non-efficient approximability. Proc. 9th Annual IEEE Conf. on Structure in Complexity Theory, 1994, pp. 356–366.

    Google Scholar 

  36. H. Hunt III, M. Marathe. V. Radhakrishnan, S. Ravi, D. Rosenkrantz and R. Stearns. Parallel approximation schemes for a class of planar and near planar combinatorial problems. Information and Computation, 173(1), Feb. 2002, pp. 40–63.

    Google Scholar 

  37. H. Hunt III, R. Stearns and M. Marathe. Relational represent ability, local reductions and the complexity of generalized satisfiability problem. submitted. Technical Report No. LA-UR-00-6108, Los Alamos National Laboratory.

    Google Scholar 

  38. H. Hunt III, M. Marathe, V. Radhakrishnan and R. Stearns. The complexity of planar counting problems. SIAM J. Computing, 27, 1998, pp. 1142–1167.

    Article  MATH  MathSciNet  Google Scholar 

  39. H. Hunt III, R. Stearns and M. Marathe. Strongly local reductions and the complexity/efficient approximability of algebra and optimization on abstract algebraic structures. International Conference on Symbolic and Algebraic Computations (ISAAC), July 2001.

    Google Scholar 

  40. H. Hunt III, M. Marathe, V. Radhakrishnan, S. Ravi, D. Rosenkrantz and R. Stearns. NC-approximation schemes for NP-and PSPACE-hard problems for geometric graphs. J. Algorithms, 26, 1998, pp. 238–274.

    Article  MATH  MathSciNet  Google Scholar 

  41. H. Hunt III, R. Jacob, M.V. Marathe, D. Rosenkrantz and R.E. Stearns. Towards syntactic characterizations of approximation schemes via predicate and graph decompositions. Technical Report No. LA-UR-97-479, Los Alamos National Laboratory, January 1997.

    Google Scholar 

  42. P. Jeavons, D. Cohen and M. Gyssens. Closure properties of constraints. J. of the ACM, (JACM) 44(4):527–548, July 1997.

    Article  MATH  MathSciNet  Google Scholar 

  43. S. Khanna, M. Sudan L. Trevisan and D. Williamson. The approximability of constraint satisfaction problems. SIAM J. on Computing, 30(6), pp. 1863–1920, March 2001.

    Google Scholar 

  44. S. Khanna and R. Motwani “Towards a syntactic characterization of PTAS” Proc. 28th Annual ACM Symposium on Theory of Computing, (STOC), pp. 329–337, Philadelphia, PA May 1996.

    Google Scholar 

  45. M. Krentel. The Complexity of optimization problems. J. Computer and System Sciences (JCSS) 36, pp. 490–509, 1988.

    Article  MATH  MathSciNet  Google Scholar 

  46. R. Ladner. Polynomial space counting problems. SIAM J. Computing, 18(6), pp. 1087–1097, 1989.

    Article  MATH  MathSciNet  Google Scholar 

  47. T. Lengauer and K. Wagner. The correlation between the complexities of non-hierarchical and hierarchical versions of graph problems. J. Computer and System Sciences (JCSS), Vol. 44, 1992, pp. 63–93.

    Article  MATH  MathSciNet  Google Scholar 

  48. D. Lichtenstein. Planar formulae and their uses. SIAM J. Computing, Vol 11, No. 2, May 1982, pp. 329–343.

    Article  MATH  MathSciNet  Google Scholar 

  49. P.D. Lincoln, J.C. Mitchell and A. Scederov. Optimization complexity of linear logic proof games. Theoretical Computer Science, 227 (1999) pp. 299–331.

    Article  MATH  MathSciNet  Google Scholar 

  50. R. Lipton and R. Tarjan. Applications of a planar separator theorem. SIAM J. Computing, 9, 1980, pp. 615–627.

    Article  MATH  MathSciNet  Google Scholar 

  51. M. Littman, S. Majercik, and T. Pitassi. Stochastic Boolean satisfiability. Journal of Artificial Intelligence, Kluwer Publications, 2000.

    Google Scholar 

  52. S. MacLane and G. Birkhoff, Algebra, Macmillan, NY 1967.

    MATH  Google Scholar 

  53. M. Marathe, H. Hunt III, D. Rosenkrantz and R. Stearns. Theory of periodically specified problems:complexity and approximability. Proc. 13th IEEE Conf. on Computational Complexity, 1998.

    Google Scholar 

  54. M. Marathe, H. Hunt III, R. Stearns and V. Radhakrishnan. Approximation algorithms for PSPACE-hard hierarchically and periodically specified problems. SIAM J. Computing, 27(5), pp. 1237–1261, Oct. 1998.

    Google Scholar 

  55. M. Marathe, H. Hunt III, R. Stearns and V. Radhakrishnan. Complexity of hierarchically and 1-dimensional periodically specified problems. AMS-DIMACS Volume Series on Discrete Mathematics and Theoretical Computer Science: Workshop on Satisfiability Problem: Theory and Application, 35, November 1997.

    Google Scholar 

  56. G. L. Miller, S. H. Teng, W. Thurston and S. A. Vavasis. Separators for sphere packings and nearest neighbor graphs. J. of the ACM (JACM), 44(1), pp. 1–29, Jan. 1997.

    Google Scholar 

  57. J. Orlin. The Complexity of dynamic/periodic languages and optimization Problems. Sloan W.P. No. 1679-86 July 1985, Working paper, Alfred P. Sloan School of Management, MIT, Cambridge, MA 02139. A Preliminary version of the paper appears in Proc. 13th ACM Annual Symposium on Theory of Computing (STOC), 1978, pp. 218–227.

    Google Scholar 

  58. A. Panconesi and D. Ranjan. Quantifiers and approximations. Theoretical Computer Science (TCS), 107, 1993, pp. 145–163.

    Article  MATH  MathSciNet  Google Scholar 

  59. C. Papadimitriou. Games against nature. J. Computer and System Sciences (JCSS), 31, 1985, pp. 288–301.

    Article  MATH  MathSciNet  Google Scholar 

  60. C. Papadimitriou. Complexity Theory. Addison-Wesley, Reading, MA, 1994.

    Google Scholar 

  61. C. Papadimitriou and M. Yannakakis. Optimization, approximation, and complexity classes. J. Computer and System Sciences (JCSS), 43, 1991, pp. 425–440.

    Article  MATH  MathSciNet  Google Scholar 

  62. C. Robinson. Dynamical Systems Stability, Symbolic Dynamics, and Chaos 2nd Edition. CRC Press, Boca Raton, Florida, 1999.

    MATH  Google Scholar 

  63. J. Saxe. Two papers on graph embedding problems. Technical Report, Dept of Comp. Science, Carnegie Mellon University, Pittsburg, CMU-CS-80-102, 1980.

    Google Scholar 

  64. T. Schaefer. The complexity of satisfiability problems. Proc. 10th Annual ACM Symposium on Theory of Computing (STOC), 1978, pp. 216–226.

    Google Scholar 

  65. C. Schnorr. Satisfiability is quasilinear complete in NQL. J. of the ACM (JACM), 25(1):136–145, January 1978.

    Google Scholar 

  66. S.K. Shukla, H.B. Hunt III, D.J. Rosenkrantz, and R.E. Stearns. On the complexity of relational problems for finite state processes. Proc. International Colloquium on Automata, Programming, and Languages (ICALP), 1996, pp. 466–477.

    Google Scholar 

  67. R. Stearns and H. Hunt III. Power indices and easier hard problems. Math. Systems Theory 23, pp. 209–225, 1990.

    Article  MATH  MathSciNet  Google Scholar 

  68. R. Stearns and H. Hunt III. An Algebraic model for combinatorial problems. SIAM J. Computing, Vol. 25, April 1996, pp. 448–476.

    Google Scholar 

  69. L. Trevisan. Reductions and (Non-)Approximability. Ph.D. Thesis, Dipartimento di Scienze dell’Informazione, University of Rome, “La Sapienza”, Italy, 1997.

    Google Scholar 

  70. L. Valiant. The complexity of enumeration and reliability problems. SIAM J. Computing, 8(3), August 1979, pp. 410–421.

    Google Scholar 

  71. D. Zuckerman. On unapproximable versions of NP-complete problems. SIAM J. Computing, 25(6), pp. 1293–1304, 1996.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Basic and Applied Simulation Science (D-2), P.O.Box 1663, MS M997, USA

    Madhav V. Marathe

  2. Los Alamos National Laboratory, Los Alamos, NM, 87545, USA

    Madhav V. Marathe

Authors
  1. Madhav V. Marathe
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Institute of Theoretical Computer Science, ETH Zentrum, ETH Zürich, 8092, Zürich, Switzerland

    Peter Widmayer  & Stephan Eidenbenz  & 

  2. Department of Languages and Sciences of the Computation E.T.S. de Ingeniería Informática, University of Málaga, Campus de Teatinos, 29071, Málaga, Spain

    Francisco Triguero , Rafael Morales  & Ricardo Conejo ,  & 

  3. School of Cognitive and Computing Sciences, University of Sussex, Falmer, Brighton, BN1 9QN, UK

    Matthew Hennessy

Rights and permissions

Reprints and permissions

Copyright information

© 2002 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Marathe, M.V. (2002). Towards a Predictive Computational Complexity Theory. In: Widmayer, P., Eidenbenz, S., Triguero, F., Morales, R., Conejo, R., Hennessy, M. (eds) Automata, Languages and Programming. ICALP 2002. Lecture Notes in Computer Science, vol 2380. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45465-9_2

Download citation

  • DOI: https://doi.org/10.1007/3-540-45465-9_2

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43864-9

  • Online ISBN: 978-3-540-45465-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation