On Feb 23, 2008, at 5:48 PM, apfelmus wrote:
Henning Thielemann wrote:
It seems that algorithms on graphs can be implemented particularly efficient in low-level languages with pointers and in-place updates. E.g. topological sort needs only linear time, provided that dereferencing pointers requires constant time. I could simulate pointer dereferencings and pointer updates by Map yielding linear logarithmic time for topological sort. I wonder if it is possible to write a linear time topological sort using lazy evaluation, since the runtime system of Haskell implementations is a graph processor based on pointers.
First of all, topological sorting is only linear time because the 32 or 64 bit used to label nodes aren't counted. Put differently, random access in constant time to a collection of n elements doesn't exist.
That being said, we want to use arrays of course. Preferably in a "whole-meal" way that doesn't involve incremental state updates. A few minutes ago, I stumbled upon the lazyarray packages which points to the paper
Thomas Johnsson. "Efficient Graph Algorithms Using Lazy Monolithic Arrays" http://citeseer.ist.psu.edu/95126.html
which offers such a way! (Although I currently don't quite understand why this works, and these ad-hoc unique numbers bother me.)
I have an implementation of this in GHC based on some of the early ST papers, if anyone is interested. It's rather old and may have bit- rotted; cabalizing it is at the top of "whenever-I-get-time", along with generic splittable supplies. Note that getting the laziness right is somewhat tricky. -Jan-Willem Maessen