Conclusion

Abstract

We hope that this monograph inspires the reader to enter into a deeper study of Distance Geometry. Our aim was to present it as an introduction to research and teaching of the subject, where our main idea was to show that the mathematical world becomes captivating when we integrate several concepts motivated by a real and challenging problem. In exploring the area of Distance Geometry, we touched upon several different mathematical and computational fields: graph theory, geometry, algebra, combinatorics, data structures, and complexity of algorithms. We also touched upon ideas such as dimension, metric, symmetry, numerical approximation, solvability of problems and computational cost.