Least-Squares Fitting of Two 3-D Point Sets
IEEE Transactions on Pattern Analysis and Machine Intelligence
SCG '94 Proceedings of the tenth annual symposium on Computational geometry
Randomized algorithms
Geometric matching under noise: combinatorial bounds and algorithms
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
On the closest string and substring problems
Journal of the ACM (JACM)
Computing Largest Common Point Sets under Approximate Congruence
ESA '00 Proceedings of the 8th Annual European Symposium on Algorithms
Finding Largest Well-Predicted Subset of Protein Structure Models
CPM '08 Proceedings of the 19th annual symposium on Combinatorial Pattern Matching
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The largest well predicted subset problem is formulated for comparison of two predicted 3D protein structures from the same sequence. Given two ordered point sets A = {a1, ..., an} and B = {b1, b2, ... bn} containing n points, and a threshold d, the largest well predicted subset problem is to find the rigid transformation T for a largest subset Bopt of B such that the distance between ai and T(bi) is at most d for every bi in Bopt. A meaningful prediction requires that the size of Bopt is at least an for some constant a [8]. We use LWPS(A,B, d, α) to denote the largest well predicted subset problem with meaningful prediction. An (1 + δ1, 1 - δ2)-approximation for LWPS(A,B, d, α) is to find a transformation T to bring a subset B′ ⊆ B of size at least (1-δ2)|Bopt| such that for each bi ∈ B′, the Euclidean distance between the two points distance(ai, T(bi)) ≤ (1 + δ1)d. We develop a constant time (1 + δ1, 1 - δ2)-approximation algorithm for LWPS(A,B, d, α) for arbitrary positive constants δ1 and δ2.