next up previous
Next: Proof Up: Optimal mapping and scheduling Previous: Optimal mapping and scheduling

Proof

Without loss of generality, assume that tex2html_wrap_inline1186 (the result is symmetric in the rows and columns), and let tex2html_wrap_inline1188. We begin the proof with the following preliminary result, where tex2html_wrap_inline1190 denotes any valid scheduling of the tiles (tex2html_wrap_inline1192 is the time-step at which the execution of I begins):


 lemma380


Jack Dongarra
Sat Feb 8 08:17:58 EST 1997