Skip to main content
SpringerLink
Log in

Space and Time Complexity of Exact Algorithms: Some Open Problems

  • Conference paper
Parameterized and Exact Computation (IWPEC 2004)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3162))

Included in the following conference series:

Abstract

We discuss open questions around worst case time and space bounds for NP-hard problems. We are interested in exponential time solutions for these problems with a relatively good worst case behavior.

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 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
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. Bax, E.T.: Inclusion and exclusion algorithm for the Hamiltonian path problem. Information Processing Letters 47, 203–207 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  2. Bax, E.T.: Algorithms to count paths and cycles. Information Processing Letters 52, 249–252 (1994)

    Article  MathSciNet  Google Scholar 

  3. Bax, E.T., Franklin, J.: A finite-difference sieve to count paths and cycles by length. Information Processing Letters 60, 171–176 (1996)

    Article  MathSciNet  Google Scholar 

  4. Ben-Or, M.: Lower bounds for algebraic computation trees. In: Proceedings of the 15th Annual ACM Symposium on the Theory of Computing (STOC 1983), pp. 80–86 (1983)

    Google Scholar 

  5. Coppersmith, D., Winograd, S.: Matrix multiplication via arithmetic progressions. Journal of Symbolic Computation 9, 251–280 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  6. Dobkin, D., Lipton, R.J.: A lower bound of \(\frac{1}{2}\) n2 on linear search programs for the knapsack problem. Journal of Computer and System Sciences 16, 413–417 (1978)

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  8. Downey, R.G., Fellows, M.R.: Parameterized complexity. Springer Monographs in Computer Science (1999)

    Google Scholar 

  9. Eisenbrand, F., Grandoni, F.: On the complexity of fixed parameter clique and dominating set. Theoretical Computer Science (2004) (to appear)

    Google Scholar 

  10. Eppstein, D.: The traveling salesman problem for cubic graphs. In: Dehne, F., Sack, J.-R., Smid, M. (eds.) WADS 2003. LNCS, vol. 2748, pp. 307–318. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  11. Erickson, J.: Lower bounds for linear satisfiability problems. Chicago Journal of Theoretical Computer Science 1999(8)

    Google Scholar 

  12. Erickson, J.: Private communication (2004)

    Google Scholar 

  13. Fedin, S.S., Kulikov, A.S.: Solution of the maximum cut problem in time 2|E|/4 (In Russian). Zapiski Nauchnykh Seminarov Sankt-Peterburgskoe Otdeleniya Matematicheskiĭ Institut imeni V.A. Steklova 293, 129–138 (2002)

    Google Scholar 

  14. Feige, U., Kilian, J.: On limited versus polynomial nondeterminism. Chicago Journal of Theoretical Computer Science (1997)

    Google Scholar 

  15. Gajentaan, A., Overmars, M.H.: On a class of O(n2) problems in computational geometry. Computational Geometry 5, 165–185 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  16. Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. Freeman, San Francisco (1979)

    MATH  Google Scholar 

  17. Held, M., Karp, R.M.: A dynamic programming approach to sequencing problems. Journal of SIAM 10, 196–210 (1962)

    MATH  MathSciNet  Google Scholar 

  18. Horowitz, E., Sahni, S.: Computing partitions with applications to the knapsack problem. Journal of the ACM 21, 277–292 (1974)

    Article  MATH  MathSciNet  Google Scholar 

  19. Itai, A., Rodeh, M.: Finding a minimum circuit in a graph. SIAM Journal on Computing 7, 413–423 (1978)

    Article  MATH  MathSciNet  Google Scholar 

  20. Karp, R.M.: Dynamic programming meets the principle of inclusion and exclusion. Operations Research Letters 1, 49–51 (1982)

    Article  MATH  MathSciNet  Google Scholar 

  21. Lawler, E.L.: A note on the complexity of the chromatic number problem. Information Processing Letters 5, 66–67 (1976)

    Article  MATH  MathSciNet  Google Scholar 

  22. Nešetřil, J., Poljak, S.: On the complexity of the subgraph problem. Commentationes Mathematicae Universitatis Carolinae 26, 415–419 (1985)

    MATH  MathSciNet  Google Scholar 

  23. Schroeppel, R., Shamir, A.: A T = O(2n/2), S = O(2n/4) algorithm for certain NP-complete problems. SIAM Journal on Computing 10, 456–464 (1981)

    Article  MATH  MathSciNet  Google Scholar 

  24. Tarjan, R.E., Trojanowski, A.E.: Finding a maximum independent set. SIAM Journal on Computing 6, 537–546 (1977)

    Article  MATH  MathSciNet  Google Scholar 

  25. Williams, R.: A new algorithm for optimal constraint satisfaction and its implications. In: Díaz, J., Karhumäki, J., Lepistö, A., Sannella, D. (eds.) ICALP 2004. LNCS, vol. 3142, pp. 1227–1237. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  26. 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 

Download references

Author information

Authors and Affiliations

  1. TU Eindhoven, The Netherlands

    Gerhard J. Woeginger

Authors
  1. Gerhard J. Woeginger
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. School of Mathematics, Statistics, and Computer Science, Victoria University, PO Box 600, Wellington, New Zealand

    Rod Downey

  2. PCRU, Office of DVC (Research), University of Newcastle, Australia

    Michael Fellows

  3. Carleton University, Ottawa, Canada

    Frank Dehne

Rights and permissions

Reprints and permissions

Copyright information

© 2004 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Woeginger, G.J. (2004). Space and Time Complexity of Exact Algorithms: Some Open Problems. In: Downey, R., Fellows, M., Dehne, F. (eds) Parameterized and Exact Computation. IWPEC 2004. Lecture Notes in Computer Science, vol 3162. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-28639-4_25

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-28639-4_25

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-23071-7

  • Online ISBN: 978-3-540-28639-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation