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What work has been done on approximation schemes for $\mathsf{P}$-complete optimization problems? Would the desired approximation algorithms here be "fully log-space approximation schemes" or "fully $\mathsf{NC}$ approximation schemes", analogous to $\mathsf{FPTAS}$ for $\mathsf{NP}$ optimization problems?

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    $\begingroup$ Why is P-completeness a relevant notion for approximations ? Are you limited to logspace in some way ? and why ? $\endgroup$ – Suresh Venkat Jan 30 '12 at 21:26
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    $\begingroup$ You might be interested in this paper: Till Tantau, Logspace Optimization Problems and Their Approximability Properties, Theory of Computing Systems 41(2), pp. 327-350 (2007), springerlink.com/content/m52274505l5344g6 $\endgroup$ – Jan Johannsen Jan 31 '12 at 8:50
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    $\begingroup$ Try searching NCAS and FNCAS. $\endgroup$ – Tsuyoshi Ito Jan 31 '12 at 14:31
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This one seems related, although it focuses more on parallel time (NC) rather than the closely related space (L): http://www.springerlink.com/content/8hn2q8lvf3ukbbx0/

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