What is the cheapest way to connect villages with fibre broadband?

AI HLAI SL Solid Also in: Geometry & Voronoi, Finance

Research question

What is the minimum total length of cable needed to connect [a group of villages] using a minimum spanning tree, and how much would adding one extra junction point (a Steiner point) save?

Adapt it: change the place, the data or the comparison until the question is yours.

Why it makes a good exploration

Utilities use minimum spanning trees to plan networks. Using real villages near you, and then discovering that adding a new point can beat the MST, is a strong, original extension.

The mathematics you'll need

Weighted graphs and minimum spanning trees
Kruskal's and Prim's algorithms (show one in full)
Distance calculations from coordinates
Steiner points and 120° angles (explain)

Course labels show where a technique sits; using maths from outside your course is fine if you explain it clearly and say it is new to you.

Where the data comes from

Village coordinates from OpenStreetMap; road distances if cables follow roads.

OpenStreetMap — Free map with exact coordinates of schools, hospitals, shops and stations; export or read off coordinates.
GeoGebra — Free geometry and graphing software — Voronoi diagrams, loci and regression built in.

Cite every source in a footnote where you use it and in your bibliography. Check the licence of any dataset you download.

A possible outline

Explain the problem and assumptions (cable along roads or straight lines).
Build the distance table.
Find the MST with one algorithm, checking with the other.
Test a Steiner point and compute the saving.
Reflect on costs, terrain and existing infrastructure.

Pitfalls that cost marks

Repeating both algorithms in full (show one).
Mixing straight-line and road distances.
No real-world check of the result.

Showing personal engagement

Choose villages near your home.
Research the real broadband rollout in the area.
Estimate the cost using published per-km figures.

See Criterion C: personal engagement for what examiners look for.

Taking it further

Find the optimal Steiner point position by minimising the total distance with calculus or technology.

Turn this idea into your IA

Plan this IAOpens the planner with this question, the maths and data sources filled in. Desmos workspacePlot your data, fit models and keep your graphs with your plan. AI feedback on a draftCriterion-by-criterion feedback with evidence from your own text. Coaching, not rewriting. Examiner reviewPete, a practising IA examiner, reads your draft and talks it through with you (€100).