DISCO -- a MATLAB software for distributed conformation of anchor-free graph realization problems

Kim-Chuan Toh, and Ngai-Hang Z. Leung.

The software was first released on 25 Nov 2009. It was last updated in 25 Nov 2009 with some minor bugs corrected. The software is designed to solve anchor-free graph realization problems based on semidefinite programming (SDP) relexation of the following nonconvex minimization problem: 
   min{ sum_{(ij)\in E} abs(norm(xi-xj)^2-dij^2) - lambda*sum_{ij} norm(xi-xj)^2 } 

   where lambda is a positive regularization parameter. The given data is 
   { dij : (ij) \in E } 
   with E being a sparse subset of the set of all short-range distances given by
   { (ij) : norm(xi-xj) <= R }, 
   and R is the cut-off radius.
For molecular conformation of protein molecules, R is typically set to 5 or 6 Angstrom.
Important note: this is a research software. It is not intended nor designed to be a general purpose software.
For more details, see:
  • N.-H. Z. Leung and K.-C. Toh, An SDP-based divide-and-conquer algorithm for large scale noisy anchor-free graph realization, SIAM J. Scientific Computing, 31 (2009), pp. 4351--4372.
  • A movie showing how the divide-and-conquer algorithm computes the conformation of a protein molecule.