Efficient way to recursively calculate dominator tree?

Question

I\'m using the Lengauer and Tarjan algorithm with path compression to calculate the dominator tree for a graph where there are millions of nodes. The algorithm is quite complex

Answer 1

Judging by the lack of comments, I guess there aren't many people on Stackoverflow with the relevent experience to help you. I'm one of those people, but I don't want such an interesting question go down with with a dull thud so I'll try and lend a hand.

My first thought is that if this graph is generated by other compilers would it be worth taking a look at an open-source compiler, like GCC, to see how it solves this problem?

My second thought is that, the main point of your question appears to be avoiding recomputing the result for the root of the tree.

What I would do is create a wrapper around each node that contains the node itself and any pre-computed data associated with that node. A new tree would then be reconstructed from the old tree recursively using these wrapper classes. As you're constructing this tree, you'd start at the root and work your way out to the leaf nodes. For each node, you'd store the result of the computation for all the ancestory thus far. That way, you should only ever have to look at the parent node and the current node data you're processing to compute the value for your new node.

I hope that helps!

Answer 2

I do not fully understand your question, but it seems to me you want to have some incremental update feature. I researched a while ago what algorithms are their but it seemed to me that there's no known way for large graphs to do this quickly (at least from a theoretical standpoint).

You may just search for "incremental updates dominator tree" to find some references.

I guess you are aware the Eclipse Memory Analyzer does use dominator trees, so this topic is not completely "owned" by the compiler community anymore :)

Answer 3

boost::lengauer_tarjan_dominator_tree_without_dfs might help.

Answer 4

Could you elaborate on what sort of graph you're starting with? I don't see how there is any difference between a graph which is a tree, and the dominator tree of that graph. Every node's parent should be its idom, and it would of course be dominated by everything above it in the tree.