Data structures and algorithms 3: multi-dimensional searching and computational geometry
Data structures and algorithms 3: multi-dimensional searching and computational geometry
Approximate decision algorithms for approximate congruence
Information Processing Letters
SCG '94 Proceedings of the tenth annual symposium on Computational geometry
Combinatorial and experimental results for randomized point matching algorithms
Proceedings of the twelfth annual symposium on Computational geometry
Improvements on bottleneck matching and related problems using geometry
Proceedings of the twelfth annual symposium on Computational geometry
RAPID: randomized pharmacophore identification for drug design
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
Fast detection of common geometric substructure in proteins
RECOMB '99 Proceedings of the third annual international conference on Computational molecular biology
RECOMB '99 Proceedings of the third annual international conference on Computational molecular biology
Geometric matching under noise: combinatorial bounds and algorithms
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
An optimal algorithm for approximate nearest neighbor searching
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
3-D Substructure Matching in Protein Molecules
CPM '92 Proceedings of the Third Annual Symposium on Combinatorial Pattern Matching
Computing Largest Common Point Sets under Approximate Congruence
ESA '00 Proceedings of the 8th Annual European Symposium on Algorithms
On Protein Structure Alignment under Distance Constraint
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
On protein structure alignment under distance constraint
Theoretical Computer Science
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
| Hi-index | 0.00 |
Identifying the common 3-D substructure between two drug or protein molecules is an important problem in synthetic drug design and molecular biology. This problem can be represented as the following geometric pattern matching problem: given two point sets A and B in three-dimensions, and a real number Ɛ 0, find the maximum cardinality subset S ⊆ A for which there is an isometry I, such that each point of I(S) is within Ɛ distance of a distinct point of B. Since it is difficult to solve this problem exactly, in this paper we have proposed several approximation algorithms with guaranteed approximation ratio. Our algorithms can be classified into two groups. In the first we extend the notion of partial decision algorithms for Ɛ-congruence of point sets in 2-D in order to approximate the size of S. All the algorithms in this class exactly satisfy the constraint imposed by Ɛ. In the second class of algorithms this constraint is satisfied only approximately. In the latter case, we improve the known approximation ratio for this class of algorithms, while keeping the time complexity unchanged. For the existing approximation ratio, we propose algorithms with substantially better running times. We also suggest several improvements of our basic algorithms, all of which have a running time of O(n8:5). These improvements consist of using randomization, and/or an approximate maximum matching scheme for bipartite graphs.