[go: up one dir, main page]
More Web Proxy on the site http://driver.im/ skip to main content
research-article

Approximation algorithms for orthogonal line centers

Published: 30 October 2023 Publication History

Abstract

The problem of k orthogonal line center is about computing a set of k axis-parallel lines for a given set of points in ℜ 2 such that the maximum among the distances between each point to its nearest line is minimized. A 2-factor approximation algorithm and a ( 5 3, 3 2 ) bi-criteria approximation algorithm is presented for the problem. Both of them are deterministic approximation algorithms using combinatorial techniques and having sub-quadratic running times.

References

[1]
Agarwal P.K., Procopiuc C.M., Approximation algorithms for projective clustering, J. Algorithms 46 (2) (2003) 115–139.
[2]
Agarwal P.K., Procopiuc C.M., Varadarajan K.R., A (1+ ɛ)-approximation algorithm for 2-line-center, Comput. Geom. 26 (2) (2003) 119–128.
[3]
Agarwal P.K., Procopiuc C.M., Varadarajan K.R., Approximation algorithms for a k-Line center, Algorithmica 42 (3) (2005) 221–230.
[4]
Aggarwal C.C., Wolf J.L., Yu P.S., Procopiuc C., Park J.S., Fast algorithms for projected clustering, SIGMOD Rec. (1999) 61–72.
[5]
Aggarwal C.C., Yu P.S., Finding generalized projected clusters in high dimensional spaces, in: Proceedings of the 2000 ACM SIGMOD International Conference on Management of Data, SIGMOD ’00, Association for Computing Machinery, 2000, pp. 70–81.
[6]
Agrawal R., Gehrke J., Gunopulos D., Raghavan P., Automatic subspace clustering of high dimensional data for data mining applications, in: Proceedings of the 1998 ACM SIGMOD International Conference on Management of Data, 27, SIGMOD ’98, Association for Computing Machinery, 1998, pp. 94–105.
[7]
Boeing G., Urban spatial order: street network orientation, configuration, and entropy, Appl. Netw. Sci. 4 (1) (2019) 67.
[8]
Călinescu G., Dumitrescu A., Karloff H., Wan P.-J., Separating points by axis-parallel lines, Internat. J. Comput. Geom. Appl. 15 (06) (2005) 575–590.
[9]
Chakraborty B., Das A.K., Das S., Mukherjee J., Approximating k-orthogonal line center, in: Combinatorial Optimization and Applications, Springer International Publishing, 2020, pp. 47–60.
[10]
Dom M., Fellows M.R., Rosamond F.A., Parameterized complexity of stabbing rectangles and squares in the plane, in: WALCOM: Algorithms and Computation, Springer Berlin Heidelberg, 2009, pp. 298–309.
[11]
Faber A., Förstner W., Detection of dominant orthogonal road structures in small scale imagery, Int. Arch. Photogramm. Remote Sens. 33 (B3/1; PART 3) (2000) 274–281.
[12]
Feldman D., Fiat A., Sharir M., Segev D., Bi-criteria linear-time approximations for generalized k-Mean/Median/Center, in: Proceedings of the Twenty-Third Annual Symposium on Computational Geometry, SCG ’07, Association for Computing Machinery, 2007, pp. 19–26.
[13]
Gaur D.R., Ibaraki T., Krishnamurti R., Constant ratio approximation algorithms for the rectangle stabbing problem and the rectilinear partitioning problem, J. Algorithms 43 (1) (2002) 138–152.
[14]
Giannopoulos P., Knauer C., Rote G., Werner D., Fixed-parameter tractability and lower bounds for stabbing problems, Comput. Geom. 46 (7) (2013) 839–860. EuroCG 2009.
[15]
Guruswami V., Saket R., On the inapproximability of vertex cover on k-Partite k-Uniform hypergraphs, in: Automata, Languages and Programming, Springer Berlin Heidelberg, 2010, pp. 360–371.
[16]
Jaromczyk J.W., Kowaluk M., The two-line center problem from a polar view: A new algorithm and data structure, in: Proceedings of the 4th International Workshop on Algorithms and Data Structures, WADS ’95, Springer-Verlag, 1995, pp. 13–25.
[17]
F. Koushanfar, S. Slijepcevic, M. Potkonjak, A. Sangiovanni-Vincentelli, Error-tolerant multimodal sensor fusion, in: IEEE CAS Workshop on Wireless Communication and Networking, 2002, pp. 5–6.
[18]
Lovász L., Plummer M.D., Matching Theory, Vol. 367, American Mathematical Soc., 2009.
[19]
Procopiuc C.M., Jones M., Agarwal P.K., Murali T.M., A Monte Carlo algorithm for fast projective clustering, in: Proceedings of the 2002 ACM SIGMOD International Conference on Management of Data, SIGMOD ’02, Association for Computing Machinery, 2002, pp. 418–427.
[20]
Renner W.D., Pugh N.O., Ross D.B., Berg R.E., Hall D.C., An algorithm for planning stereotactic brain implants, Int. J. Radiat. Oncol. Biol. Phys. 13 (4) (1987) 631–637.
[21]
Tansel B.C., Francis R.L., Lowe T.J., State of the art-location on networks: A survey. Part I: The p-Center and p-Median problems, Manage. Sci. 29 (4) (1983).
[22]
Zanjirani Farahani R., Hekmatfar M., Facility location: Concepts, models, algorithms and case studies, Media (2009).

Cited By

View all
  • (2024)Minimum-Width Double-Slabs and Widest Empty Slabs in High DimensionsLATIN 2024: Theoretical Informatics10.1007/978-3-031-55598-5_20(303-317)Online publication date: 18-Mar-2024

Recommendations

Comments

Please enable JavaScript to view thecomments powered by Disqus.

Information & Contributors

Information

Published In

cover image Discrete Applied Mathematics
Discrete Applied Mathematics  Volume 338, Issue C
Oct 2023
347 pages

Publisher

Elsevier Science Publishers B. V.

Netherlands

Publication History

Published: 30 October 2023

Author Tags

  1. Orthogonal line centers
  2. Facility location
  3. Bi-criteria approximation
  4. Geometric optimization
  5. Combinatorial optimization

Qualifiers

  • Research-article

Contributors

Other Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

  • Downloads (Last 12 months)0
  • Downloads (Last 6 weeks)0
Reflects downloads up to 26 Dec 2024

Other Metrics

Citations

Cited By

View all
  • (2024)Minimum-Width Double-Slabs and Widest Empty Slabs in High DimensionsLATIN 2024: Theoretical Informatics10.1007/978-3-031-55598-5_20(303-317)Online publication date: 18-Mar-2024

View Options

View options

Media

Figures

Other

Tables

Share

Share

Share this Publication link

Share on social media