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. 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. IIRC it was something like 4..5 times as many of 2 sets of a million or so random Ints. But even in favourable circumstances (tree elements are boxed Ints) divide and conquer on AVL trees seemed much faster than Hedge on Data.Set. Of course ideally we would want implementations of Hedge for AVL and divide and conquer for Data.Set too, but I didn't feel inclined to write them. Regards -- Adrian Hey