Conditions for unique graph realizations
SIAM Journal on Computing
Reconstructing a three-dimensional model with arbitrary errors
Journal of the ACM (JACM)
Molecular Modeling and Simulation: An Interdisciplinary Guide
Molecular Modeling and Simulation: An Interdisciplinary Guide
Journal of Global Optimization
Discrete & Computational Geometry
Semidefinite programming based algorithms for sensor network localization
ACM Transactions on Sensor Networks (TOSN)
Theory of semidefinite programming for Sensor Network Localization
Mathematical Programming: Series A and B
MD-jeep: an implementation of a branch and prune algorithm for distance geometry problems
ICMS'10 Proceedings of the Third international congress conference on Mathematical software
A parallel version of the Branch & Prune algorithm for the Molecular Distance Geometry Problem
AICCSA '10 Proceedings of the ACS/IEEE International Conference on Computer Systems and Applications - AICCSA 2010
On the computation of protein backbones by using artificial backbones of hydrogens
Journal of Global Optimization
Sphere and dot product representations of graphs
Proceedings of the twenty-seventh annual symposium on Computational geometry
On the number of solutions of the discretizable molecular distance geometry problem
COCOA'11 Proceedings of the 5th international conference on Combinatorial optimization and applications
An artificial backbone of hydrogens for finding the conformation of protein molecules
BIBMW '09 Proceedings of the 2009 IEEE International Conference on Bioinformatics and Biomedicine Workshop
Universal Rigidity and Edge Sparsification for Sensor Network Localization
SIAM Journal on Optimization
The discretizable molecular distance geometry problem
Computational Optimization and Applications
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Several application fields require finding Euclidean coordinates consistent with a set of distances. More precisely, given a simple undirected edge-weighted graph, we wish to find a realization in a Euclidean space so that adjacent vertices are placed at a distance which is equal to the corresponding edge weight. Realizations of a graph can be either flexible or rigid. In certain cases, rigidity can be seen as a property of the graph rather than the realization. In the last decade, several advances have been made in graph rigidity, but most of these, for applicative reasons, focus on graphs having a unique realization. In this paper we consider a particular type of weighted Henneberg graphs that model protein backbones and show that almost all of them give rise to sets of incongruent realizations whose cardinality is a power of two.