Document Open Access Logo

Approximate Minimum-Weight Matching with Outliers Under Translation

Authors Pankaj K. Agarwal, Haim Kaplan, Geva Kipper, Wolfgang Mulzer , Günter Rote , Micha Sharir, Allen Xiao

PDF

File

Thumbnail PDF
PDF
LIPIcs.ISAAC.2018.26.pdf
  • Filesize: 0.52 MB
  • 13 pages

Document Identifiers

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Combinatorics
Keywords
  • Minimum-weight partial matching
  • Pattern matching
  • Approximation

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads
    0
    Metadata Views

Abstract

Our goal is to compare two planar point sets by finding subsets of a given size such that a minimum-weight matching between them has the smallest weight. This can be done by a translation of one set that minimizes the weight of the matching. We give efficient algorithms (a) for finding approximately optimal matchings, when the cost of a matching is the L_p-norm of the tuple of the Euclidean distances between the pairs of matched points, for any p in [1,infty], and (b) for constructing small-size approximate minimization (or matching) diagrams: partitions of the translation space into regions, together with an approximate optimal matching for each region.

Cite As Get BibTex

Pankaj K. Agarwal, Haim Kaplan, Geva Kipper, Wolfgang Mulzer, Günter Rote, Micha Sharir, and Allen Xiao. Approximate Minimum-Weight Matching with Outliers Under Translation. In 29th International Symposium on Algorithms and Computation (ISAAC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 123, pp. 26:1-26:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018) https://doi.org/10.4230/LIPIcs.ISAAC.2018.26

Author Details

Pankaj K. Agarwal
  • Department of Computer Science, Duke University, Durham, NC 27708, USA
Haim Kaplan
  • School of Computer Science, Tel Aviv University, Tel Aviv 69978, Israel
Geva Kipper
  • School of Computer Science, Tel Aviv University, Tel Aviv 69978, Israel
Wolfgang Mulzer
  • Institut für Informatik, Freie Universität Berlin, 14195 Berlin, Germany
Günter Rote
  • Institut für Informatik, Freie Universität Berlin, 14195 Berlin, Germany
Micha Sharir
  • School of Computer Science, Tel Aviv University, Tel Aviv 69978, Israel
Allen Xiao
  • Department of Computer Science, Duke University, Durham, NC 27708, USA

Funding

Work on this paper was supported by grant 2012/229 from the U.S. - Israel Binational Science Foundation and by grant 1367/2016 from the German-Israeli Science Foundation (GIF).
  • Agarwal, Pankaj K.: Partially supported by NSF grants CCF-15-13816, CCF-15-46392, IIS-14-08846 and ARO grant W911NF-15-1-0408.
  • Mulzer, Wolfgang: Partially supported by DFG grant MU/3501/1 and ERC STG 757609.
  • Sharir, Micha: Partially supported by ISF Grant 892/13, by the Israeli Centers of Research Excellence (I-CORE) program (Center No. 4/11), by the Blavatnik Research Fund in Computer Science at Tel Aviv University, and by the Hermann Minkowski-MINERVA Center for Geometry at Tel Aviv University.
  • Xiao, Allen: Partially supported by NSF CCF-15-13816, CCF-15-46392, IIS-14-08846 and ARO grant W911NF-15-1-0408.

References

  1. Pankaj K. Agarwal, Alon Efrat, and Micha Sharir. Vertical decomposition of shallow levels in 3-dimensional arrangements and its applications. SIAM J. Comput., 29(3):912-953, 1999. Google Scholar
  2. Helmut Alt and Leonidas J. Guibas. Discrete geometric shapes: Matching, interpolation, and approximation. In J.R. Sack and J. Urrutia, editors, Handbook of Comput. Geom., pages 121-153. Elsevier, Amsterdam, 1999. Google Scholar
  3. Rinat Ben-Avraham, Matthias Henze, Rafel Jaume, Balázs Keszegh, Orit E. Raz, Micha Sharir, and Igor Tubis. Partial-Matching RMS Distance Under Translation: Combinatorics and Algorithms. Algorithmica, 80(8):2400-2421, 2018. Google Scholar
  4. Sergio Cabello, Panos Giannopoulos, Christian Knauer, and Günter Rote. Matching point sets with respect to the Earth Mover’s Distance. Comput. Geom., 39(2):118-133, 2008. Google Scholar
  5. Paz Carmi, Shlomi Dolev, Sariel Har-Peled, Matthew J. Katz, and Michael Segal. Geographic Quorum System Approximations. Algorithmica, 41(4):233-244, 2005. Google Scholar
  6. Harold N. Gabow and Robert Endre Tarjan. Faster Scaling Algorithms for Network Problems. SIAM J. Comput., 18(5):1013-1036, 1989. Google Scholar
  7. Andrew V. Goldberg, Sagi Hed, Haim Kaplan, and Robert E. Tarjan. Minimum-Cost Flows in Unit-Capacity Networks. Theory Comput. Syst., 61(4):987-1010, 2017. Google Scholar
  8. Matthias Henze, Rafel Jaume, and Balázs Keszegh. On the complexity of the partial least-squares matching Voronoi diagram. In Proc. 29th European Workshop Comput. Geom. (EWCG), pages 193-196, 2013. Google Scholar
  9. Haim Kaplan, Wolfgang Mulzer, Liam Roditty, Paul Seiferth, and Micha Sharir. Dynamic Planar Voronoi Diagrams for General Distance Functions and their Algorithmic Applications. In Proc. 28th Annu. ACM-SIAM Sympos. Discrete Algorithms (SODA), pages 2495-2504, 2017. Google Scholar
  10. Jeff M. Phillips and Pankaj K. Agarwal. On Bipartite Matching under the RMS Distance. In Proc. 18th Canad. Conf. Comput. Geom. (CCCG), pages 143-146, 2006. Google Scholar
  11. Günter Rote. Partial least-squares point matching under translations. In Proc. 26th European Workshop Comput. Geom. (EWCG), pages 249-251, 2010. Google Scholar
  12. R. Sharathkumar and Pankaj K. Agarwal. A near-linear time ε-approximation algorithm for geometric bipartite matching. In Proc. 44th Annu. ACM Sympos. Theory Comput. (STOC), pages 385-394, 2012. Google Scholar
  13. R. Sharathkumar and Pankaj K. Agarwal. Algorithms for the transportation problem in geometric settings. In Proc. 23rd Annu. ACM-SIAM Sympos. Discrete Algorithms (SODA), pages 306-317, 2012. Google Scholar
  14. Kasturi R. Varadarajan and Pankaj K. Agarwal. Approximation Algorithms for Bipartite and Non-Bipartite Matching in the Plane. In Proc. 10th Annu. ACM-SIAM Sympos. Discrete Algorithms (SODA), pages 805-814, 1999. Google Scholar
  15. Remco C. Veltkamp. Shape matching: Similarity measures and algorithms. In Proc. Intl. Conf. Shape Modeling and Applications, pages 188-197, 2001. Google Scholar
Any Issues?
X

Feedback on the Current Page

CAPTCHA

Thanks for your feedback!

Feedback submitted to Dagstuhl Publishing

Could not send message

Please try again later or send an E-mail
© 2023-2025 Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact