Extension to incomplete distance graphs

Extend the benign-landscape results for the complete-graph squared-stress objective to incomplete Euclidean distance graphs, particularly globally or universally rigid frameworks with only a subset of pairwise distances observed.

Background

The main results apply only when every pairwise distance is known. In incomplete graphs, the squared-stress objective uses only the observed edges, and the corresponding stress matrix may fail to be positive semidefinite, which is a central ingredient in the complete-graph proof.

The paper identifies globally and universally rigid incomplete frameworks as the meaningful target because only in those settings does minimizing squared stress correspond to a well-posed recovery problem. The authors mention lateration frameworks as an important structured class, but no general extension is established.