On Apr 26, 2008, at 7:41 AM, Adrian Hey wrote:
Jan-Willem Maessen wrote:
On Apr 24, 2008, at 11:33 AM, Adrian Hey wrote:
Also, if you're likely to be using union/intersection a lot you should know that Data.Map/Set are very slow for this because they use the not efficient hedge algorithm :-) OK, I'm going to bite here: What's the efficient algorithm for union on balanced trees, given that hedge union was chosen as being more efficient than naive alternatives (split and merge, repeated insertion)? My going hypothesis has been "hedge union is an inefficient algorithm, except that it's better than all those other inefficient algorithms".
Divide and conquer seems to be the most efficient, though not the algorithm presented in the Adams paper.
Just to clarify: divide and conquer splits one tree on the root value of the other (possibly avoiding enforcing the balance metric until after joining trees, though not obvious how / if that's useful)? The definition of "divide and conquer" on trees without a fixed structure is rather unclear, which is why the question comes up in the first place.
Hedge algorithm performs many more comparisons than are needed, which is obviously bad if you don't know how expensive those comparisons are going to be.
That makes sense. I found myself having the same kinds of thoughts when reading Knuth's analyses of (eg) different binary search algorithms in TAOCP v.3; if comparison was the dominant cost, which algorithm looked best suddenly changed. -Jan