1. Node Overlap Removal by Growing a Tree
Lev Nachmanson, Arlind Nocaj , Sergey Bereg , Leishi Zhang, and
Alexander Holroyd

2. What is an overlap removal algorithm?

3. Scaling does not always work

4. Related work
Dwyer, Tim, Kim Marriott, and Peter J. Stuckey. "Fast node overlap removal." International Symposium on Graph Drawing. Springer Berlin Heidelberg, 2005.
Gansner, Emden R., and Yifan Hu. "Efficient node overlap removal using a proximity stress model." International Symposium on Graph Drawing. Springer Berlin Heidelberg, 2008.
Both are fast, but the first one produces extreme aspect ratios. PRISM, is the name of second method. We believe it is the most used today algorithm.

5. PRISM = proximity stress model
PRISM = proximity stress model. EP is the set of edges of the Delaunay triangulation of the node centers, xi -the node center, dij- the ideal distance.
min

6. Tree growing idea

7. Build a Minimum Spanning Tree on a Delaunay triangulation of the node centers, by assigning edges with overlaps small cost
Grow the tree
Repeat if there are overlaps

13. Comparison with PRISM
PRISM Original GTree

14. PRISM Original GTree

15. Edge length dissimilarity Procrustes statistic K-closest neighbors
We implemented PRISM inside of MSAGL and GTree inside of Dot. We looked at
Edge length dissimilarity
Procrustes statistic
K-closest neighbors
The area
Struggle to capture the structure

16. GTree runs asymptotically faster and, in our experiments, up to 10 times faster
Requires more area
Slightly better in the quality measures.
Seems better preserving the initial “structure”
Simple to implement!

17. Why does it converge so fast?
Proof of convergence?
What is a measure that captures the layout structure preservation?

18. Thank you for your attention!