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My work is based on algorithm A that is actually a developed version of algorithm B. When I cite algorithm A, should I also cite algorithm B?

Due to the conference page limit, I prefer not to cite algorithm B, as A has already cited B and I do have cited A. Does my this "citation chain" work?

Another dilemma to me is when algorithm C incorporates (not develops) algorithm B, given the fact that I have to cite C anyway and actually I have used algorithm B, can I choose to only cite C without B? (again, to save space)

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    There are better ways to save space. – JeffE Oct 27 '13 at 20:20
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Space savings aside, your choice in this must be guided by two factors: help the readers understand what your work is built upon, and acknowledge scientific contributions of your predecessors.

With those principles in mind, I would say the choice depends on the relationship between A and B, and whether either (or both) are well-known. Let's take two simple cases to illustrate:

  • if algorithm B is world-famous, and algorithm A is a not-so-well-known extension (e.g., because it is specially optimized for a specific type of data): you will have to cite both, as you cannot assume that all readers are familiar with algorithm A.

    Herein we highlight an extension of the Abersmith algorithm,[ref A] which is itself based on the Borodin sort algorithm with specific improvements for the handling of p-adic input.

  • if algorithm A is very well known in your field, and algorithm B was an earlier algorithm that was almost completely superseded by A and little used nowadays (except for historical considerations): it is not useful to cite B.

  • So your case 1 is my case. My work is a direct application of algorithm A that is based on world-famous B. I will definitely have to cite A, since I directly adopt the method with some minor modifications. I also must cite the world-famous B? – Sibbs Gambling Oct 27 '13 at 12:50
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    Yes, you have to give (even in a few words) the reader a short introduction to A, which means you have to introduce B (and cite it) – F'x Oct 27 '13 at 12:53

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