Skip to main content
SpringerLink
Log in
Book cover

International Computing and Combinatorics Conference

COCOON 2003: Computing and Combinatorics pp 130–138Cite as

The Structure and Number of Global Roundings of a Graph

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2697))

Abstract

Given a connected weighted graph G = (V,E), we consider a hypergraph H G = (V,P G) corresponding to the set of all shortest paths in G. For a given real assignment a on V satisfying 0 ≤ a(v) ≤ 1, a global rounding α with respect to H G is a binary assignment satisfying that |Σv∈F a(v) − α(v)| < 1 for every F ∈ P G. We conjecture that there are at most |V| + 1 global roundings for H G, and also the set of global roundings is an affine independent set. We give several positive evidences for the conjecture.

This is a preview of subscription content, 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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. T. Asano, N. Katoh, K. Obokata, and T. Tokuyama, Matrix Rounding under the L p-Discrepancy Measure and Its Application to Digital Halftoning, Proc. 13th ACM-SIAM SODA (2002) pp. 896–904.

    Google Scholar 

  2. T. Asano, T. Matsui, and T. Tokuyama, Optimal Roundings of Sequences and Matrices, Nordic Journal of Computing 7 (2000) pp.241–256. (Preliminary version in SWAT00).

    MATH  MathSciNet  Google Scholar 

  3. T. Asano and T. Tokuyama, How to Color a Checkerboard with a Given Distribution — Matrix Rounding Achieving Low 2 × 2 Discrepancy, Proc. 12th ISAAC, LNCS 2223 (2001) pp. 636–648.

    Google Scholar 

  4. J. Beck and V. T. Sós, Discrepancy Theory, in Handbook of Combinatorics Volume II (ed. T. Graham, M. Grötshel, and L. Lovász) 1995, Elsevier.

    Google Scholar 

  5. B. Bollobás. Modern Graph Theory, GTM 184, Springer-Verlag, 1998.

    Google Scholar 

  6. B. Chazelle, The Discrepancy Method: Randomness and Complexity, Princeton University, 2000.

    Google Scholar 

  7. B. Doerr, Lattice Approximation and Linear Discrepancy of Totally Unimodular Matrices, Proc. 12th ACM-SIAM SODA (2001) pp.119–125.

    Google Scholar 

  8. A. Hoffman and G. Kruskal, Integral Boundary Points of Convex Polyhedra, In Linear Inequalities and Related Systems (ed. W. Kuhn and A. Tucker) (1956) pp. 223–246.

    Google Scholar 

  9. J. Jansson and T. Tokuyama, Semi-Balanced Coloring of Graphs-2-Colorings Based on a Relaxed Discrepancy Condition, Submitted.

    Google Scholar 

  10. J. Matoušek, Geometric Discrepancy, Algorithms and Combinatorics 18, Springer Verlag 1999.

    Google Scholar 

  11. H. Niederreiter, Random Number Generations and Quasi Monte Carlo Methods, CBMS-NSF Regional Conference Series in Applied Math., SIAM, 1992.

    Google Scholar 

  12. J. Pach and P. Agarwal, Combinatorial Geometry, John-Wiley & Sons, 1995.

    Google Scholar 

  13. K. Sadakane, N. Takki-Chebihi, and T. Tokuyama, Combinatorics and Algorithms on Low-Discrepancy Roundings of a Real Sequence, Proc. 28th ICALP, LNCS 2076 (2001) pp. 166–177.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Information Science, Japan Advanced Institute of Science and Technology, Tatsunokuchi, Japan

    Tetsuo Asano

  2. Graduate School of Engineering, Kyoto University, Kyoto, Japan

    Naoki Katoh

  3. Meiji University, Kawasaki, Japan

    Hisao Tamaki

  4. GSIS, Tohoku University, Sendai, Japan

    Takeshi Tokuyama

Authors
  1. Tetsuo Asano
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Naoki Katoh
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Hisao Tamaki
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Takeshi Tokuyama
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Texas at Austin, One University Station, C0500, Austin, TX, 78712, USA

    Tandy Warnow

  2. Department of Computer Science, Montana State University, EPS 357, Bozeman, MT, 59717, USA

    Binhai Zhu

Rights and permissions

Reprints and permissions

Copyright information

© 2003 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Asano, T., Katoh, N., Tamaki, H., Tokuyama, T. (2003). The Structure and Number of Global Roundings of a Graph. In: Warnow, T., Zhu, B. (eds) Computing and Combinatorics. COCOON 2003. Lecture Notes in Computer Science, vol 2697. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45071-8_15

Download citation

  • DOI: https://doi.org/10.1007/3-540-45071-8_15

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40534-4

  • Online ISBN: 978-3-540-45071-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation