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On Tue, Apr 25, 2017 at 6:17 PM, Hongbin Zheng <etherzhhb@gmail.com> wrote:

Hi Daniel,

I mean "\*As a set\*, B + C dominate D".

On Tue, Apr 25, 2017 at 5:42 PM, Daniel Berlin <dberlin@dberlin.org> wrote:

When you say collectively, you mean "would dominate it if considered a single block together?

IE

A

/ \\

B C

\\ /

D

As a set, B + C dominate D.

The set you are looking for there is (i believe):

For each predecessor, walk the idom tree until you hit NCA of all predecessors.

What do you mean by NCA?

Nearest common ancestor

If you have dfs numbers for the dom tree, you can do this very fast.

While you walk it, place all nodes on each branch in a set.

Any set that collectively dominates D must contain at least one member from each of these set, or be on the idom path between NCA and root.

IE above, it would be that

Set 1 = {B}

Set 2 = {C}

Set IDOM to root = {A}.

If you find something in "set IDOM to root", the answer is always "yes", since that block alone dominates it, the collective set must dominate it.

(unless you use a stricter definition of collective)

For the tree

A

/ \\

B D

| |

C E

\\ /

F

Set 1 = {B, C}

Set 2 = {D, E}

set IDOM to root = {A}

Thanks a lot

Hongbin