A Distributed SDP Approach for Large-Scale Noisy Anchor-Free Graph Realization with Applications to Molecular Conformation

We propose a distributed algorithm for solving Euclidean metric realization problems arising from large 3D graphs, using only noisy distance information, and without any prior knowledge of the positions of any of the vertices. In our distributed algorithm, the graph is first subdivided into smaller subgraphs using intelligent clustering methods. Then a semidefinite programming relaxation and gradient search method is used to localize each subgraph. Finally, a stitching algorithm is used to find affine maps between adjacent clusters and the positions of all points in a global coordinate system are then derived. In particular, we apply our method to the problem of finding the 3D molecular configurations of proteins based on a limited number of given pairwise distances between atoms. The protein molecules, all with known molecular configurations, are taken from the Protein Data Bank. Our algorithm is able to reconstruct reliably and efficiently the configurations of large protein molecul...

• Type: Journal
• Year: 2008
• Where: SIAMSC
• Authors: Pratik Biswas, Kim-Chuan Toh, Yinyu Ye
• Keywords: Distributed Algorithm, Molecular Configurations, Pairwise Distances, SIAMSC 2008