Congruence, similarity and symmetries of geometric objects
Discrete & Computational Geometry - ACM Symposium on Computational Geometry, Waterloo
The translation square map and approximate congruence
Information Processing Letters
Approximate decision algorithms for approximate congruence
Information Processing Letters
Approximate decision algorithms for point set congruence
SCG '92 Proceedings of the eighth annual symposium on Computational geometry
Reverse search for enumeration
Discrete Applied Mathematics - Special volume: first international colloquium on graphs and optimization (GOI), 1992
Geometric pattern matching under Euclidean motion
Computational Geometry: Theory and Applications - Special issue: computational geometry, theory and applications
On determining the congruence of point sets in d dimensions
Computational Geometry: Theory and Applications
Combinatorial and experimental results for randomized point matching algorithms
Selected papers from the 12th annual symposium on Computational Geometry
Geometric matching under noise: combinatorial bounds and algorithms
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
On the approximation of largest common subtrees and largest common point sets
Theoretical Computer Science
Approximate congruence in nearly linear time
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Output-Sensitive Cell Enumeration in Hyperplane Arrangements
SWAT '98 Proceedings of the 6th Scandinavian Workshop on Algorithm Theory
Generalized Approzimate Algorithms for Point Set Congruence
WADS '93 Proceedings of the Third Workshop on Algorithms and Data Structures
Approximation Algorithms for 3-D Commom Substructure Identification in Drug and Protein Molecules
WADS '99 Proceedings of the 6th International Workshop on Algorithms and Data Structures
Pattern Matching for Spatial Point Sets
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Finding Largest Well-Predicted Subset of Protein Structure Models
CPM '08 Proceedings of the 19th annual symposium on Combinatorial Pattern Matching
On Protein Structure Alignment under Distance Constraint
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Constant time approximation scheme for largest well predicted subset
COCOON'10 Proceedings of the 16th annual international conference on Computing and combinatorics
Applications of dimensionality reduction and exponential sums to graph automorphism
Theoretical Computer Science
On protein structure alignment under distance constraint
Theoretical Computer Science
Optimizing a Widely Used Protein Structure Alignment Measure in Expected Polynomial Time
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
On Complexity of Protein Structure Alignment Problem under Distance Constraint
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
MAPPIS: multiple 3D alignment of protein-protein interfaces
CompLife'05 Proceedings of the First international conference on Computational Life Sciences
Recognition of binding patterns common to a set of protein structures
RECOMB'05 Proceedings of the 9th Annual international conference on Research in Computational Molecular Biology
An efficient approximation algorithm for point pattern matching under noise
LATIN'06 Proceedings of the 7th Latin American conference on Theoretical Informatics
DALIX: Optimal DALI Protein Structure Alignment
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Improved Algorithms for Matching r-Separated Sets with Applications to Protein Structure Alignment
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
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The problem of computing a largest common point set (LCP) between two point sets under Ɛ-congruence with the bottleneck matching metric has recently been a subject of extensive study. Although polynomial time solutions are known for the planar case and for restricted sets of transformations and metrics (like translations and the Hausdorff-metric under L∞-norm), no complexity results are formally known for the general problem. In this paper we give polynomial time algorithms for this problem under different classes of transformations and metrics for any fixed dimension, and establish NP-hardness for unbounded dimensions. Any solution to this (or related) problem, especially in higher dimensions, is generally believed to involve implementation difficulties because they rely on the computation of intersections between algebraic surfaces. We show that (contrary to intuitive expectations) this problem can be solved under a rational arithmetic model in a straightforward manner if the set of transformations is extended to general affine transformations under the L∞-norm (difficulty of this problem is generally expected to be in the order: translations