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I am working on an interesting algorithm: Its absolute error is exponential in a parameter $j \in \mathbb{N}$, and for a given $j$, I have complete freedom to choose between an $\mathcal{O}(1)$ time-complexity algorithm with memory consumption ${\sim}2^{j}$, or a $\mathcal{O}(2^j)$ time-complexity algorithm with $\mathcal{O}(1)$ memory consumption. I can also "meet in the middle" and consume any intermediate amount of memory and compute that I wish.

I'm having trouble deciding on how make the compute/memory/accuracy tradeoffs. Have there been cost functions developed that could help answer this question?

Obviously, I could write something like $$ \mathrm{cost} = c_1 t + c_2 m + c_3 e $$ for evaluation time $t$, memory consumption $m$ and error $e$, and just pick three positive constants $c_1, c_2, c_3$. But I would prefer to use a cost function that someone has already put some thought into.

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  • $\begingroup$ If you can modify the behaviour with parameters (as opposed to being to reprogram the whole algorithm), this is a good time to employ an autotuner. Determining the best trade-off from purely theoretical concerns will almost certainly give suboptimal performance. $\endgroup$ – Richard Mar 1 at 22:32
  • $\begingroup$ @Richard: Do you have a recommendation for an autotuner? $\endgroup$ – user14717 Mar 1 at 22:41

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