Euclidean Distance Matrix Completion Tools
Column Approximate Minimum Degree Permutation
Dissimilarity Parameterization Formulation
Linear Matrix Operator
Linear Matrix Operator
Euclidean Distance Matrix Completion
Create a Point Configuration from a Distance Matrix
Linear Matrix Operator
Guided Random Search
Compute Minimum Spanning Tree
Minimum Spanning Tree Preserving Lower Bound
Shortest Path Upper Bound
Nonparametric Position Formulation
Minimum Spanning Tree Path
Linear Matrix Operator
Relaxed Guided Random Search
Semi-Definite Programming Algorithm
Sensor Network Localization
Semidefinite Programming-based Protein Structure Determination
Implements various general algorithms to estimate missing elements of a Euclidean (squared) distance matrix. Includes optimization methods based on semi-definite programming found in Alfakih, Khadani, and Wolkowicz (1999)<doi:10.1023/A:1008655427845>, a non-convex position formulation by Fang and O'Leary (2012)<doi:10.1080/10556788.2011.643888>, and a dissimilarity parameterization formulation by Trosset (2000)<doi:10.1023/A:1008722907820>. When the only non-missing distances are those on the minimal spanning tree, the guided random search algorithm will complete the matrix while preserving the minimal spanning tree following Rahman and Oldford (2018)<doi:10.1137/16M1092350>. Point configurations in specified dimensions can be determined from the completions. Special problems such as the sensor localization problem, as for example in Krislock and Wolkowicz (2010)<doi:10.1137/090759392>, as well as reconstructing the geometry of a molecular structure, as for example in Hendrickson (1995)<doi:10.1137/0805040>, can also be solved. These and other methods are described in the thesis of Adam Rahman(2018)<https://hdl.handle.net/10012/13365>.