The molecule problem: Determining conformation from pairwise distances
The molecule problem is that of determining the coordinates of a set of points in space from a (usually sparse) set of pairwise distance measurements. As its name implies, it has applications in the determination of molecular conformation. Unfortunately, the molecule problem is NP-hard. The author presents an approach to the molecule problem that uses a very specialized divide-and-conquer technique. Instead of solving a single large problem he tries to solve a sequence of smaller, presumably easier ones. These smaller problems consist of subsets of points whose relative locations can be determined uniquely. Once such a subset is positioned, its points can collectively be treated as a rigid body. This can greatly reduce the number degrees of freedom in the problem. Identifying subsets of points whose relative locations can be uniquely determined requires exploiting some very special structure inherent in the molecule problem. He reduces this identification to a purely combinatoric characterization that ignores the actual distances. He develops necessary graph theoretic conditions for a set of points to have a unique solution, along with efficient algorithms to find subgraphs with these properties. These characterizations and algorithms combine ideas from matching theory, differential topology and matrix computations. These ideas have been implemented in ABBIE, a program to solve three-dimensional instances of the molecule problem. ABBIE combines the recursive decomposition described above with a nonlinear global optimizer to perform the coordinate determinations. Details of this implementation are described, and numerical results of simulated chemical data are presented.
- Research Organization:
- Cornell Univ., Ithaca, NY (United States)
- OSTI ID:
- 5856813
- Resource Relation:
- Other Information: Thesis (Ph.D)
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
MOLECULAR STRUCTURE
A CODES
ALGORITHMS
CONFORMAL MAPPING
DATA
DEGREES OF FREEDOM
DIFFERENTIAL TOPOLOGY
MATHEMATICS
MATRICES
COMPUTER CODES
INFORMATION
MAPPING
MATHEMATICAL LOGIC
TOPOLOGICAL MAPPING
TOPOLOGY
TRANSFORMATIONS
990200* - Mathematics & Computers