The complexity of minimizing wire lengths in VLSI layouts
Information Processing Letters
Unit-length embedding of binary trees on a square grid
Information Processing Letters
The logic engine and the realization problem for nearest neighbor graphs
Theoretical Computer Science - Special issue on theoretical computer science in Australia and New Zealand
Graph Drawing: Algorithms for the Visualization of Graphs
Graph Drawing: Algorithms for the Visualization of Graphs
Expansion of layouts of complete binary trees into grids
Discrete Applied Mathematics
3D chip stacking with C4 technology
IBM Journal of Research and Development
3D chip-stacking technology with through-silicon vias and low-volume lead-free interconnections
IBM Journal of Research and Development
| Hi-index | 5.23 |
Deciding whether a graph can be embedded in a grid using only unit-length edges is NP-complete, even when restricted to binary trees. However, it is not difficult to devise a number of graph classes for which the problem is polynomial, even trivial. A natural step, outstanding thus far, was to provide a broad classification of graphs that make for polynomial or NP-complete instances. We provide such a classification based on the set of allowed vertex degrees in the input graphs, yielding a full dichotomy on the complexity of the problem. As byproducts, the previous NP-completeness result for binary trees was strengthened to strictly binary trees, and the three-dimensional version of the problem was for the first time proven to be NP-complete. Our results were made possible by introducing the concepts of consistent orientations and robust gadgets, and by showing how the former allows NP-completeness proofs by local replacement even in the absence of the latter.