Shortest-path problems and molecular conformation
Discrete Applied Mathematics - Applications of Graphs in Chemistry and Physics
Probabilistic construction of deterministic algorithms: approximating packing integer programs
Journal of Computer and System Sciences - 27th IEEE Conference on Foundations of Computer Science October 27-29, 1986
Bound smoothing under chirality constraints
SIAM Journal on Discrete Mathematics
The molecule problem: determining conformation from pairwise distances
The molecule problem: determining conformation from pairwise distances
Conditions for unique graph realizations
SIAM Journal on Computing
Extremal Graph Theory
CSB '05 Proceedings of the 2005 IEEE Computational Systems Bioinformatics Conference
An Algebraic Geometry Approach to Protein Structure Determination from NMR Data
CSB '05 Proceedings of the 2005 IEEE Computational Systems Bioinformatics Conference
Plane embeddings of planar graph metrics
Proceedings of the twenty-second annual symposium on Computational geometry
Localization in sparse networks using sweeps
Proceedings of the 12th annual international conference on Mobile computing and networking
The discretizable molecular distance geometry problem
Computational Optimization and Applications
On the number of realizations of certain Henneberg graphs arising in protein conformation
Discrete Applied Mathematics
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A number of current technologies allow for the determination of interatomic distance information in structures such as proteins and RNA. Thus, the reconstruction of a three-dimensional set of points using information about its interpoint distances has become a task of basic importance in determining molecular structure. The distance measurements one obtains from techniques such as NMR are typically sparse and error-prone, greatly complicating the reconstruction task. Many of these errors result in distance measurements that can be safely assumed to lie within certain fixed tolerances. But a number of sources of systematic error in these experiments lead to inaccuracies in the data that are very hard to quantify; in effect, one must treat certain entries of the measured distance matrix as being arbitrarily “corrupted.”The existence of arbitrary errors leads to an interesting sort of error-correction problem—how many corrupted entries in a distance matrix can be efficiently corrected to produce a consistent three-dimensional structure? For the case of an n × n matrix in which every entry is specified, we provide a randomized algorithm running in time O(n log n) that enumerates all structures consistent with at most (1/2-&egr;)n errors per row, with high probability. In the case of randomly located errors, we can correct errors of the same density in a sparse matrix-one in which only a &bgr; fraction of the entries in each row are given, for any constant &bgr;gt;0.