1) The only direct references to "algorithmic diagnostic methods" on google were gastro-intestinal sites that said, basically, "Algorithmic diagnostic methods guide an examiner through the examination process informing him about necessary application of stimulating/blocking medicaments or provoking actions. "
2) That tells me basically they're saying, discuss methodical diagnosis (i.e. I'm tier 2 or 3 support and I've given the front-line helpdesk folks a list of questions to ask in order to help diagnose the problem.)
3) Is this a term your teacher used in class? Maybe they should try using industry standard terminology! :-) (I hate academic sorts of folks.)
4) #665 would be across the street from the devil, not next door! :-P (At least, thats how it works in America.)

-C