Learn Spanish (Latin America): Queremos un algoritmo que sea muy eficiente. - We want an algorithm that is very efficient.

Because we are talking about an algorithm that we want to find, but we don't know if it actually exists yet. When you describe something that is unknown, hypothetical, or indefinite (notice we used un algoritmo instead of el algoritmo), Spanish uses the subjunctive for the description.

Would the sentence change if we already had a specific algorithm in mind?

Yes! If you are talking about a specific, known algorithm that you already have, you would use the indicative. For example, Tenemos el algoritmo que es muy eficiente means 'We have the algorithm that is very efficient.'

Does the verb queremos automatically force the subjunctive here?

Not automatically, but verbs of desire like querer, necesitar (to need), and buscar (to look for) almost always set up this exact situation. Because you want or need something you don't possess yet, it naturally creates the 'unknown' scenario that requires the subjunctive in the que clause.

How does this connect to impersonal expressions like es lógico que, which we are also learning?

Impersonal expressions trigger the subjunctive because they state an opinion, emotion, or evaluation about an action, rather than declaring a hard fact. Similarly, this sentence uses the subjunctive because it expresses a desire for an unknown thing. Both structures use the subjunctive because they deal with ideas and subjectivity rather than stating objective reality.