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Approximate Minimum-Weight Matching with Outliers Under Translation

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

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

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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

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