Approximation Algorithms for 3-d Common Substructure Identiication in Drug and Protein Molecules
نویسندگان
چکیده
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 > 0, nd the maximum cardinality subset S A for which there is an isometry I, such that each point of I(S) is within distance of a distinct point of B. Since it is diicult to solve this problem exactly, in this paper we have proposed several approximation algorithms with guaranteed approximation ratio. Our algorithms can be classiied into two groups. In the rst we extend the notion of partial decision algorithms for-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. In the second class of algorithms this constraint is satissed 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(n 8:5). These improvements consist of using randomization, and/or an approximate maximum matching scheme for bipartite graphs.
منابع مشابه
Approximation Algorithms for 3-D Commom Substructure Identification in Drug and Protein Molecules
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