How do the sparse consolidation algorithm helps to improve the Cognos TM1 performance?
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what is sparse consolidation algorithm? – deebee May 02 '12 at 00:31
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I found a concise description here:
Cognos TM1 Rules – how do they really work?
During consolidations, TM1 uses a sparse consolidation algorithm to skip over cells that contain zero or are empty. This algorithm speeds up consolidation calculations in cubes that are highly sparse.

Craig T
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A comprehensive post on TM1 rules and consolidation: Skipcheck Feeders in TM1
It gives step by step process on how rules and consolidation works in TM1 and how skipcheck and feeders are used to improve the calculation speed.