Rather than distinguish between types of related problems using words like “fundamental”, “applied”, and “real”, which don’t convey anything beyond what the reader wants them to convey, I was looking for more useful terms. Terms that classified problems and conveyed their relationships in a factual, non-judgmental and familiar way.

Given that I spend so much of my research time on graphs and trees, that is where I started. After some work I came up with this tree:

A summary of the problem classes, with elevator definitions, and related examples, follows:

• Root problems have no domain-specific form. Integer Programming is an example.
• A Core problem is one whose form many people are familiar with; whose structure has been extensively studied; which is likely to contribute to the complexity of derived problems. The Traveling Salesperson Problem is such a problem.
• A Trunk problem adds some domain-specific detail to a core problem, but is still very generic. The Vehicle Routing Problem with Time Windows is an example.
• A Branch problem is a specialized  trunk problem with domain considerations requiring significant amounts of original modeling, often requiring specialized solution procedures. A capacitated pickup and delivery problem would fall into this category.
• A Leaf problem is highly specialized, usually with a customer in mind, including high levels of detail. Scheduling trucks for Fedex would fall into this category.

The problem in the paper I am working on is a trunk problem: Udine Timetabling. It adds “wrinkles” to the Graph Coloring problem, a core problem. Most problems starting with a “the” are core problems; usually if there is “green” involved, it is a leaf problem.

Obvious other examples include: Metaheuristics as root problems; The Karp 21 as core problems (0-1 IP and 3SAT are probably root problems).

I am curious about whether people think this taxonomy is useful; whether they would suggest changes; and where they think the problems they are working on go on the tree.