Skip to main content
SpringerLink
Log in

Optimizing a 2D Function Satisfying Unimodality Properties

  • Conference paper
Algorithms – ESA 2005 (ESA 2005)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3669))

Included in the following conference series:

Abstract

The number of probes needed by the best possible algorithm for locally or globally optimizing a bivariate function varies substantially depending on the assumptions made about the function. We consider a wide variety of assumptions—in particular, global unimodality, unimodality of rows and/or columns, and total unimodality—and prove tight or nearly tight upper and lower bounds in all cases. Our results include both nontrivial optimization algorithms and nontrivial adversary arguments depending on the scenario.

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. Aggarwal, A., Klawe, M.M., Moran, S., Shor, P.W., Wilber, R.: Geometric applications of a matrix-searching algorithm. Algorithmica 2, 195–208 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  2. Althöfer, I., Koschnick, K.-U.: On the deterministic complexity of searching local maxima. Discrete Appl. Math. 43(2), 111–113 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  3. Edelsbrunner, H.: Computing the extreme distances between two convex polygons. J. Algorithms 6, 213–224 (1985)

    Article  MATH  MathSciNet  Google Scholar 

  4. Galil, Z., Park, K.: Dynamic programming with convexity, concavity and sparsity. Theoret. Computer Sci. 92(1), 49–76 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  5. Gärtner, B., Morris, W.D., Rüst, L.: Unique sink orientations of grids. In: Jünger, M., Kaibel, V. (eds.) IPCO 2005. LNCS, vol. 3509, pp. 210–224. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  6. Kiefer, J.: Sequential minimax search for a maximum. Proc. Amer. Math. Soc. 4, 502–506 (1953)

    Article  MATH  MathSciNet  Google Scholar 

  7. Llewellyn, D.C., Tovey, C., Trick, M.: Local optimization on graphs. Discrete Appl. Math. 23(2), 157–178 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  8. Llewellyn, D.C., Tovey, C.A.: Dividing and conquering the square. Discrete Appl. Math. 43(2), 131–153 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  9. Mityagin, A.: On the complexity of finding a local maximum of functions on discrete planar subsets. Theoret. Computer Sci. 310(1-3), 355–363 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  10. Tovey, C.A.: Local improvement on discrete structures. In: Local Search in Combinatorial Optimization, pp. 57–89. John Wiley and Sons, Chichester (1997)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. MIT Computer Science and Artificial Intelligence Laboratory, 32 Vassar Street, Cambridge, MA, 02139, USA

    Erik D. Demaine

  2. Département d’informatique, Université Libre de Bruxelles, ULB, CP212, Bruxelles, Belgium

    Stefan Langerman

Authors
  1. Erik D. Demaine
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Stefan Langerman
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. BRICS, MADALGO, Department of Computer Science, University of Aarhus, Denmark

    Gerth Stølting Brodal

  2. University of Rome “La Sapienza”, Rome, Italy

    Stefano Leonardi

Rights and permissions

Reprints and permissions

Copyright information

© 2005 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Demaine, E.D., Langerman, S. (2005). Optimizing a 2D Function Satisfying Unimodality Properties. In: Brodal, G.S., Leonardi, S. (eds) Algorithms – ESA 2005. ESA 2005. Lecture Notes in Computer Science, vol 3669. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11561071_78

Download citation

  • DOI: https://doi.org/10.1007/11561071_78

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-29118-3

  • Online ISBN: 978-3-540-31951-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation