Top-down vs Bottom-up approaches in describing an algorithm in a research paper
The answer depends on personal preferences, as well as on the algorithm itself. Consider the following two descriptions of SOLVE_PROBLEM:

Top-down: We want to solve problem A on input. Function SOLVE_PROBLEM solves the problem. There are two cases, depending on condition B, which we can check with function CHECK. If the condition holds, we solve the problem with FUNCTION_1. Otherwise we use FUNCTION_2.

Bottom-up: We want to solve problem A on input. In the general case, the problem can be solved with FUNCTION_1. The general solution assumes condition B, which we can check with function CHECK. If the condition does not hold, we can solve the special case with FUNCTION_2. This completes function SOLVE_PROBLEM.

I personally prefer the top-down approach, if the algorithm has multiple equally important parts. Bottom-up approach becomes preferable, if one part of the algorithm attacks the core of the problem, while the rest just deals with special cases and administrative stuff.