Articles once more

[nyggus]

Hi:
I know that this issue was discussed at the forum recently, but I need to be sure and convinced. In the phrase
1. “the particular algorithm’s step…,”
“the” refers to algorithm, doesn’t it? Then, there is nothing said whether a step is defined or not, and this information is not required in this sentence. Am I right?
Some other examples:
2. “a clustering problem,” “a clustering algorithm”—it is incorrect, since before clustering (a noun) one shouldn’t put an indefinite article;
3. “the procedure’s effect”—“the” refers to the procedure;
4. “a decomposition’s result” (in the meaning “a result of decomposition”)—it is incorrect again, since decomposition is uncountable.

Thanks,
Nyggus

[Casiopea]

Either 'the' or 'a':

1. “the particular algorithm’s step…,”
=> the particular algorithm you're talking about

2. “the clustering problem,” “the clustering algorithm”
=> the clustering problem you're talking about

3. “the procedure’s effect”
=> the procedure you're talking about

4. “the decomposition’s result”
=> the result of the decomposition you're talking about