Skip to main content
SpringerLink
Log in

Monomial Testing and Applications

  • Conference paper
Frontiers in Algorithmics and Algorithmic Aspects in Information and Management

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7924))

  • 946 Accesses

Abstract

In this paper, we devise two algorithms for the problem of testing q-monomials of degree k in any multivariate polynomial represented by a circuit, regardless of the primality of q. One is an O *(2k) time randomized algorithm. The other is an O *(12.8k) time deterministic algorithm for the same q-monomial testing problem but requiring the polynomials to be represented by tree-like circuits. Several applications of q-monomial testing are also given, including a deterministic O *(12.8mk) upper bound for the m-set k-packing problem.

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. Abasi, H., Bshouty, N.: A simple algorithm for undirected hamiltonicity, ECCC, Report No. 12 (2013)

    Google Scholar 

  2. Chen, S., Chen, Y., Yang, Q.: Towards randomized testing of q-monomials in multivariate polynomials (January 2013) (manuscript), http://arxiv.org/abs/1302.5898

  3. Björklund, A.: Determinant sums for undirected hamilonicity. In: Proceedings of the 51th IEEE Foundations of Computer Science (FOCS 2010), pp. 173–182 (2010)

    Google Scholar 

  4. Björklund, A., Husfeldt, T., Kaski, P., Koivisto, M.: Narrow sieves for parameterized paths and packings. arXiv:1007.1161v1 (2010)

    Google Scholar 

  5. Blum, M., Kannan, S.: Designing programs that check their work. J. ACM 42(1), 269–291 (1995)

    Article  MATH  Google Scholar 

  6. Chen, Z., Fu, B.: Approximating Multilinear Monomial Coefficients and Maximum Multilinear Monomials in Multivariate Polynomials. J. Comb. Optim. 25(2), 234–254 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  7. Chen, Z., Fu, B.: The Complexity of Testing Monomials in Multivariate Polynomials. In: Wang, W., Zhu, X., Du, D.-Z. (eds.) COCOA 2011. LNCS, vol. 6831, pp. 1–15. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  8. Chen, Z., Fu, B.: Approximating Multilinear Monomial Coefficients and Maximum Multilinear Monomials in Multivariate Polynomials. In: Wu, W., Daescu, O. (eds.) COCOA 2010, Part I. LNCS, vol. 6508, pp. 309–323. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  9. Chen, Z., Fu, B., Liu, Y., Schweller, R.T.: On Testing Monomials in Multivariate Polynomials. Theoretical Computer Science (April 13, 2012) (forthcoming), doi:10.1016/j.tcs.2012.03.038

    Google Scholar 

  10. Chen, Z., Fu, B., Liu, Y., Schweller, R.: Algorithms for Testing Monomials in Multivariate Polynomials. In: Wang, W., Zhu, X., Du, D.-Z. (eds.) COCOA 2011. LNCS, vol. 6831, pp. 16–30. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  11. Chen, J., Lu, S., Sze, S.-H., Zhang, F.: Improved algorithms for path, matching, and packing problems. In: SODA, pp. 298–307 (2007)

    Google Scholar 

  12. Fellows, M.R., Knauer, C., Nishimura, N., Ragde, P., Rosamond, F., Stege, U., Thilikos, D.M., Whitesides, S.: Faster fixed-parameter tractable algorithms for matching and packing problems. Algorithmica 52(2), 167–176 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  13. Koutis, I.: Faster algebraic algorithms for path and packing problems. In: Aceto, L., Damgård, I., Goldberg, L.A., Halldórsson, M.M., Ingólfsdóttir, A., Walukiewicz, I. (eds.) ICALP 2008, Part I. LNCS, vol. 5125, pp. 575–586. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  14. Motwani, R., Raghavan, P.: Randomized Algorithms. Cambridge University Press (1995)

    Google Scholar 

  15. Naor, M., Schulman, L.J., Srinivasan, A.: Splitters and near-optimal derandomization. In: FOCS, pp. 182–191 (1995)

    Google Scholar 

  16. Raz, R., Shpilka, A.: Deterministic polynomial identity testing in non-commutative models. Computational Complexity 14(1), 1–19 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  17. Williams, R.: Finding paths of length k in O *(2k) time. Information Processing Letters 109, 315–318 (2009)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, University of Texas-Pan American, Edinburg, TX, 78539, USA

    Shenshi Chen

Authors
  1. Shenshi Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. School of Engineering and Information Technology, Charles Darwin University, 0909, Darwin, NT, Australia

    Michael Fellows

  2. School of High-Technology for Human Welfare, Tokai University, 317 Nishimo, 410-0395, Numazu, Japan

    Xuehou Tan

  3. Department of Computer Science, Montana State University, 59717, Bozeman, MT, USA

    Binhai Zhu

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Chen, S. (2013). Monomial Testing and Applications. In: Fellows, M., Tan, X., Zhu, B. (eds) Frontiers in Algorithmics and Algorithmic Aspects in Information and Management. Lecture Notes in Computer Science, vol 7924. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38756-2_13

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-38756-2_13

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-38755-5

  • Online ISBN: 978-3-642-38756-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation