Minimum partial-matching and hausdorff RMS-distance under translation: Combinatorics and algorithms

Rinat Ben-Avraham, Matthias Henze, Rafel Jaume, Balázs Keszegh, Orit E. Raz, Micha Sharir, Igor Tubis

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

9 Scopus citations


We consider the RMS-distance (sum of squared distances between pairs of points) under translation between two point sets in the plane. In the Hausdorff setup, each point is paired to its nearest neighbor in the other set. We develop algorithms for finding a local minimum in near-linear time on the line, and in nearly quadratic time in the plane. These improve substantially the worst-case behavior of the popular ICP heuristics for solving this problem. In the partial-matching setup, each point in the smaller set is matched to a distinct point in the bigger set. Although the problem is not known to be polynomial, we establish several structural properties of the underlying subdivision of the plane and derive improved bounds on its complexity. In addition, we show how to compute a local minimum of the partial-matching RMS-distance under translation, in polynomial time.

Original languageAmerican English
Title of host publicationAlgorithms, ESA 2014 - 22nd Annual European Symposium, Proceedings
PublisherSpringer Verlag
Number of pages12
ISBN (Print)9783662447765
StatePublished - 2014
Externally publishedYes
Event22nd Annual European Symposium on Algorithms, ESA 2014 - Wroclaw, Poland
Duration: 8 Sep 201410 Sep 2014

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume8737 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference22nd Annual European Symposium on Algorithms, ESA 2014


  • Hausdorff RMS-distance
  • local minimum
  • partial matching
  • polyhedral subdivision


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