# The Reingold-Tilford algorithm revisited

A while ago, as part of early research into what became my MSc project, I wrote code to create and then draw red-black trees using C++.

To draw the trees I used the venerable Reingold-Tilford algorithm, which is more or less the standard approach. I wrote some blogs about it and pages here seem to come pretty high up in Google searches for the algorithm, so I get passing traffic regularly as a result.

But idly chasing these links has led me to a chapter from the forthcoming Handbook of Graph Drawing and Visualization edited by Roberto Tamassia which has a chapter on tree drawing by Adrian Rusu, which contains bad news for us Reingold-Tilford fan boys, as this summary from the book of an experiment comparing algorithmic performance shows (emphasis added):

• The performance of a drawing algorithm on a tree-type is not a good predictor of the performance of the same algorithm on other tree-types: some of the algorithms perform best on a tree-type, and worst on other tree-types.
Reingold-Tilford algorithm [RT81] scores worse in comparison to the other chosen algorithms for almost all ten aesthetics considered.
• The intuition that low average edge length and area go together is contradicted in only one case.
• The intuitions that average edge length and maximum edge length, uniform edge length and total edge length, and short maximum edge length and close farthest leaf go together are contradicted for unbalanced binary trees.
• With regards to area, of the four algorithms studied, three perform best on diﬀerent types of trees.
• With regards to aspect ratio, of the four algorithms studied, three perform well on trees of diﬀerent types and sizes.
• Not all algorithms studied perform best on complete binary trees even though they have one of the simplest tree structures.
The level-based algorithm of Reingold-Tilford [RT81] produces much worse aspect ratios than algorithms designed using other approaches.
• The path-based algorithm of Chan et al. [CGKT02] tends to construct drawings with better area at the expense of worse aspect ratio.