Skip to main content
SpringerLink
Log in

Improved Algorithm for a Widest 1-Corner Corridor

  • Conference paper
WALCOM: Algorithms and Computation (WALCOM 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5431))

Included in the following conference series:

  • 850 Accesses

Abstract

Given a set P of n points on a 2D plane, the 1-corner empty corridor is a region inside the convex hull of P which is bounded by a pair of links; each link is an unbounded trapezium bounded by two parallel half-lines, and it does not contain any point of P. We present an improved algorithm for computing the widest empty 1-corner corridor that runs in O(n 3log2 n) time and O(n 2) space. This improves the time complexity of the best known algorithm for the same problem by a factor of \(\frac{n}{\log n}\)[4].

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. Chen, S.-W.: Widest empty L-shaped corridor. Information Processing Letters 58, 277–283 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  2. Chattopadhyay, S., Das, P.P.: The k-dense corridor problem. Pattern Recognition Letters 11, 463–469 (1990)

    Article  MATH  Google Scholar 

  3. Diaz-Banez, J.M., Hurtado, F.: Computing obnoxious 1-corner polygonal chains. Computers and Operations Research 33, 1117–1128 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  4. Diaz-Banez, J.M., Lopez, M.A., Sellares, J.A.: On finding a widest empty 1-corner corridor. Information Processing Letters 98, 199–205 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  5. Goswami, P.P., Das, S., Nandy, S.C.: Triangular range counting query in 2D and its application in finding k nearest neighbors of a line segment. Computational Geometry Theory and Applications 29, 163–175 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  6. Houle, M.E., Maciel, A.: Finding the widest empty corridor through a set of points. In: Toussaint, G. (ed.) Snapshots of Computational and Discrete Geometry, Technical Report SOCS-88.11, School of Computer Science, McGill University (1988)

    Google Scholar 

  7. Janardan, R., Preparata, F.P.: Widest-corridor problem. Nordic J. Computing 1, 231–245 (1994)

    MathSciNet  Google Scholar 

  8. Lee, D.T., Ching, Y.T.: The Power of Geometric Duality Revisited. Information Processing Letter 21, 117–122 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  9. Nandy, S.C., Harayama, T., Asano, T.: Dynamically maintaining the widest k-dense corridor. Theoretical Computer Science 255, 627–639 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  10. Shin, C.-S., Shin, S.Y., Chwa, K.-Y.: The widest k-dense corridor problem. Information Processing Letters 68, 25–31 (1998)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. TOR ANUMANA Technologies Private Limited, Kolkata, 700020, India

    Gautam K. Das

  2. Rebaca Technologies Private Limited, Kolkata, 700 091, India

    Debapriyay Mukhopadhyay

  3. Indian Statistical Institute, Kolkata, 700108, India

    Subhas C. Nandy

Authors
  1. Gautam K. Das
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Debapriyay Mukhopadhyay
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Subhas C. Nandy
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Indian Statistical Institute, 700 108, Kolkata, India

    Sandip Das

  2. Japan Advanced Institute of Science and Technology, 923-1292, Ishikawa, Japan

    Ryuhei Uehara

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Das, G.K., Mukhopadhyay, D., Nandy, S.C. (2009). Improved Algorithm for a Widest 1-Corner Corridor. In: Das, S., Uehara, R. (eds) WALCOM: Algorithms and Computation. WALCOM 2009. Lecture Notes in Computer Science, vol 5431. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00202-1_8

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-00202-1_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-00201-4

  • Online ISBN: 978-3-642-00202-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation