A greedy approach to the BU HUB requirements
"The BU Hub is Boston University’s University-wide general education program that emphasizes working across disciplines to prepare for a complex and diverse world. Students can explore a variety of courses and innovative learning experiences while developing six essential capacities and fulfilling Hub requirements. Explore these six capacities, Hub learning outcomes, and how the Hub works below." -https://www.bu.edu/hub/hub-courses/
├── README.md
├── catalog
│ ├── catalog.json (full catalog scraped from the BU course catalog)
│ └── catalog_sorted.json (all HUB courses as of fall 2020 - 100-level and up)
│
├── search.js (catalog in JavaScript for easy map/reduce/filter-ing)
│
└── set_cover.py (the actual algorithm)
BU students know how annoying the HUB is, and how confusing it is to ensure they aren't forgetting any requirements, as even one overlooked unit necessitates a whole extra 4 credit class.
One way to formulate the BU HUB course selection problem is as a graph problem. Given a graph G={U,V,E}, let U be the available courses, V be the set of required HUB units, and E connect courses to the units they fulfill. A solution is any subset of U that collectively neighbors all of V.
Unfortunately this description is of an NP-complete problem, as it is mutually reducible to ordinary set coverage. And even though we may be able to narrow down BUs thousands of courses to a couple hundred, it's still intractable to solve exhaustively—or guarantee the most optimal solution.
Thankfully however, we don't necessarily need to guarantee most optimal course-selection, just a good enough one for a recommendation, and there's a nice little greedy algorithm for finding sets that are pretty close if not indeed correct on occasion.
The reduction to make use of this algorithm is simply rewriting the courses as sets of the HUB units they provide and remembering to look up the indexes of the chosen classes at the end.
Often, there is more than one most optimal solution, and we can run the algorithm again over a differently ordering of the catalog to see the others. Alternatively if the algorithm fails to find a good-enough solution on the sorted list, where the easiest classes would get considered first, we can rerun it nondeterministically on randomly shuffled inputs until it either halts with a great schedule, or our patience runs out. It can take as many as 400+ tries sometimes on the default set with strict requirements, so don't always expect a loop.
Social Inquiry and Scientific Inquiry are not both required—only one of them. Thankfully this is easily fixable with a quick preprocessing step, which combines the two into a "Social/Scientific Inquiry II" as a single unit. Managing doubled requirements, however, does not have such a simple reduction, and I took the naive (but not unbearably inefficient) approach of rerunning the algorithm until it finds a selection with the desired multiplicity of HUB units (for example "Writing-Intensive Course" is needed twice).
Number of courses offering each unit
------------------------------------
5 First-Year Writing Seminar
11 Writing, Research, and Inquiry
65 Scientific Inquiry II
73 Quantitative Reasoning I
77 Scientific Inquiry I
82 Quantitative Reasoning II
84 Philosophical Inquiry and Life's Meanings
97 Digital/Multimedia Expression
110 Social Inquiry II
132 Creativity/Innovation
134 Social Inquiry I
146 Ethical Reasoning
158 Oral and/or Signed Communication
167 Teamwork/Collaboration
183 Writing-Intensive Course
209 The Individual in Community
223 Research and Information Literacy
273 Historical Consciousness
286 Aesthetic Exploration
296 Global Citizenship and Intercultural Literacy
320 Critical ThinkingRun set_cover.py in your favorite python interpreter. You will want to edit the file and fill in which HUB units are already completed.