There is no universally optimal algorithm for applying do-calculus to identity causal effect most efficiently, as the optimal approach will depend on the specific context and circumstances of the problem. Do-calculus is a mathematical framework that can be used to identify and estimate causal effects, but the specific algorithms and methods used to apply do-calculus will vary depending on the characteristics of the data and the research question.

The computational cost of applying do-calculus will also vary depending on the specific algorithm and method used, as well as the size and complexity of the data. In general, do-calculus algorithms can require significant computational resources, particularly when dealing with large or complex datasets.

There are several variants of do-calculus, including the original do-calculus developed by Judea Pearl, as well as other frameworks such as the counterfactual do-calculus and the potential outcome do-calculus. These variants have different assumptions and approaches, and can be used in different contexts to identify and estimate causal effects.

Overall, while there are algorithms and methods that can be used to apply do-calculus to identity causal effect, there is no universally optimal algorithm for doing so. The specific approach and computational cost will vary depending on the context and characteristics of the problem. There are also several variants of do-calculus that can be used in different contexts.