Skip to main content
SpringerLink
Log in

Generalized Class Cover Problem with Axis-Parallel Strips

  • Conference paper
Algorithms and Computation (WALCOM 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8344))

Included in the following conference series:

  • 1091 Accesses

Abstract

We initiate the study of a generalization of the class cover problem [1,2], the generalized class cover problem, where we are allowed to misclassify some points provided we pay an associated positive penalty for every misclassified point. We study five different variants of generalized class cover problem with axis-parallel strips and half-strips in the plane, thus extending similar work by Bereg et al. [2] on the class cover problem. For each of these variants, we either show that they are in P, or prove that they are NP-complete and give constant factor approximation algorithms.

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. Cannon, A.H., Cowen, L.J.: Approximation algorithms for the class cover problem. Annals of Mathematics and Artificial Intelligence 40(3-4), 215–223 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  2. Bereg, S., Cabello, S., Díaz-Báñez, J.M., Pérez-Lantero, P., Seara, C., Ventura, I.: The class cover problem with boxes. Computational Geometry 45(7), 294–304 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  3. Brönnimann, H., Goodrich, M.T.: Almost optimal set covers in finite VC-dimension. Discrete & Computational Geometry 14(1), 463–479 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  4. Matoušek, J., Seidel, R., Welzl, E.: How to net a lot with little: small ε-nets for disks and halfspaces. In: Proc. of the 6th Annual Symposium on Computational Geometry, SCG 1990, pp. 16–22. ACM (1990)

    Google Scholar 

  5. Clarkson, K.L., Varadarajan, K.: Improved approximation algorithms for geometric set cover. Discrete & Computational Geometry 37(1), 43–58 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  6. Mustafa, N.H., Ray, S.: Improved results on geometric hitting set problems. Discrete & Computational Geometry 44(4), 883–895 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  7. Aschner, R., Katz, M.J., Morgenstern, G., Yuditsky, Y.: Approximation schemes for covering and packing. In: Ghosh, S.K., Tokuyama, T. (eds.) WALCOM 2013. LNCS, vol. 7748, pp. 89–100. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  8. Gibson, M., Pirwani, I.A.: Algorithms for dominating set in disk graphs: Breaking the logn barrier. In: de Berg, M., Meyer, U. (eds.) ESA 2010, Part I. LNCS, vol. 6346, pp. 243–254. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  9. Carr, R.D., Doddi, S., Konjevod, G., Marathe, M.: On the red-blue set cover problem. In: Proc. of 11th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2000, pp. 345–353 (2000)

    Google Scholar 

  10. Chan, T.M., Hu, N.: Geometric red-blue set cover for unit squares and related problems. In: Proceedings of the 25th Canadian Conference on Computational Geometry, CCCG 2013, pp. 289–293 (2013)

    Google Scholar 

  11. Chin, F.Y.L., Ting, H.-F., Zhang, Y.: Variable-size rectangle covering. In: Du, D.-Z., Hu, X., Pardalos, P.M. (eds.) COCOA 2009. LNCS, vol. 5573, pp. 145–154. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  12. Lovász, L.: Submodular functions and convexity. In: Bachem, A., Korte, B., Grötschel, M. (eds.) Mathematical Programming The State of the Art, pp. 235–257. Springer, Heidelberg (1983)

    Chapter  Google Scholar 

  13. Iwata, S., Nagano, K.: Submodular function minimization under covering constraints. In: 50th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2009, Atlanta, Georgia, USA, October 25-27, pp. 671–680 (2009)

    Google Scholar 

  14. Schrijver, A.: A combinatorial algorithm minimizing submodular functions in strongly polynomial time. Journal of Combinatorial Theory, Series B 80(2), 346–355 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  15. Delong, A., Veksler, O., Osokin, A., Boykov, Y.: Minimizing sparse high-order energies by submodular vertex-cover. Advances in Neural Information Processing Systems 25, 971–979 (2012)

    Google Scholar 

  16. Goel, G., Karande, C., Tripathi, P., Wang, L.: Approximability of combinatorial problems with multi-agent submodular cost functions. In: FOCS 2009: Proceedings of 50th Annual IEEE Symposium on Foundations of Computer Science (2009)

    Google Scholar 

  17. Garey, M.R., Johnson, D.S.: Computers and Intractability; A Guide to the Theory of NP-Completeness. W. H. Freeman & Co., New York (1990)

    Google Scholar 

  18. Gaur, D.R., Ibaraki, T., Krishnamurti, R.: Constant ratio approximation algorithms for the rectangle stabbing problem and the rectilinear partitioning problem. Journal of Algorithms 43(1), 138–152 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  19. Chan, T.M., Grant, E., Könemann, J., Sharpe, M.: Weighted capacitated, priority, and geometric set cover via improved quasi-uniform sampling. In: Proc. of the 13th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2012, pp. 1576–1585 (2012)

    Google Scholar 

  20. Bienstock, D., Goemans, M., Simchi-Levi, D., Williamson, D.: A note on the prize collecting traveling salesman problem. Mathematical Programming 59(1-3), 413–420 (1993)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science and Engineering, Indian Institute of Technology Ropar, Nangal Road, Rupnagar, Punjab, 140001, India

    Apurva Mudgal & Supantha Pandit

Authors
  1. Apurva Mudgal
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Supantha Pandit
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Computer Science and Engineering, Indian Institute of Technology Kharagpur, 721302, Kharagpur, India

    Sudebkumar Prasant Pal

  2. National Institute of Informatics, 2-1-2 Hitotsubashi, 101-8430, Chiyoda-ku, Tokyo, Japan

    Kunihiko Sadakane

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer International Publishing Switzerland

About this paper

Cite this paper

Mudgal, A., Pandit, S. (2014). Generalized Class Cover Problem with Axis-Parallel Strips. In: Pal, S.P., Sadakane, K. (eds) Algorithms and Computation. WALCOM 2014. Lecture Notes in Computer Science, vol 8344. Springer, Cham. https://doi.org/10.1007/978-3-319-04657-0_4

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-04657-0_4

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-04656-3

  • Online ISBN: 978-3-319-04657-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation