Dice Question Streamline Icon: https://streamlinehq.com

Complexity of Partial Drawing Extensibility

Determine whether the Partial Drawing Extensibility problem is ER-complete: given a partial straight-line embedding of a graph, decide whether it can be extended to a straight-line embedding of the entire graph.

Information Square Streamline Icon: https://streamlinehq.com

Background

Partial Drawing Extensibility (PDE) asks if a straight-line drawing specified for a subset of vertices can be extended to a full straight-line planar embedding of the graph.

The survey identifies PDE as a central unresolved problem in geometric graph drawing and notes only ER-hardness via the variant where realization must lie within a polygonal domain.

References

A tantalizing and fundamental open question in this area is the complexity of the partial drawing extensibility problem: Is it -complete to test whether a partial straight-line embedding of a graph can be extended to a straight-line embedding of the full graph? The problem is only known to be -hard if the realization has to lie within a polygon.

— The Existential Theory of the Reals as a Complexity Class: A Compendium (2407.18006 - Schaefer et al., 25 Jul 2024) in Section “Graph Drawing”