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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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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.

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

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.

Subject Classification

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

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References

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