Re: Is register allocation really NP-Complete?

In article <11422.27ef7017@zeus.unomaha.edu> payne@zeus.unomaha.edu (Matt Payne) writes:
>
>So, I'm confused. [Chow 90] implies that this is a NP-complete problem,
>but how can it be if [Chow 90]'s interference graphs are interval
>graphs?


Conflict graphs, even coarse ones such as Chow constructs, are not
interval graphs. Consider the fragment:


A =
                B =
      l: ... = B
... = A
C =
...
... = C
B =
goto l;


... A


Note that the live range of B is discontiguous due to the control flow.
These live ranges might be viewed as:


   BB CCC B
AAAAAAAAAAA


and so we see the conflict graph is not an interval graph.


However, I don't know of a method that shows how to construct a program
whose conflict graph corresponds to some arbitrary graph and so it is
still possible that the restricted coloring problem associated with
conflict graphs is not NP-hard.
--
David Callahan (david@tera.com, david@june.cs.washington.edu,david@rice.edu)
Tera Computer Co. 400 North 34th Street Seattle WA, 98103
--

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