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From The Free On-line Dictionary of Computing (05 January 2017) [foldoc]:
register allocation
The phase of a compiler that
determines which values will be placed in registers.
Register allocation may be combined with {register
assignment}.
This problem can be shown to be isomorphic to {graph
colouring} by relating values to nodes in the graph and
registers to colours. Values (nodes) which must be valid
simultaneously are linked by edges and cannot be stored in the
same register (coloured the same).
See also register dancing and register spilling.
[Preston Briggs, PhD thesis, Rice University, April 1992
{"Register Allocation via Graph Coloring"
(ftp://ftp.cs.rice.edu/public/preston/thesis.ps.gz)}].
(2000-12-04)