Solution: GigaFibre in Lincolnshire and Yorkshire

The plan for GigaFibre’s network in the Lincolnshire region can be designed using Kruskal’s algorithm. Below is a list of connections ordered by the associated distance. Notice that there are three connections each with the same distance. Depending on how you order these edges will potentially result in a different solution, however the sum of the chosen connections will be the same.

Source	Destination	Distance
Grantham	Sleaford	18
Spalding	Boston	23
Sleaford	Boston	23
Sleaford	Spalding	23
Skegness	Boston	31
Sleaford	Lincoln	33
Grantham	Spalding	35
Grantham	Lincoln	36
Lincoln	Scunthorpe	39
Lincoln	Grimsby	47
Grimsby	Skegness	53
Lincoln	Skegness	59
Grantham	Sheffield	75

Assuming that the connections are order in the table above then a potential solution would be to include the connections between Sheffield and Grantham, Grantham and Sleaford, Sleaford and Boston, Boston and Spalding, Boston and Skegness, Sleaford and Lincoln, Lincoln and Grimsby and Lincoln and Scunthorpe. The sum of the connected included in the solution is 289. The illustration below indicates the connections which are included in an economical solution to the problem.

A full text description of the illustration is available below:

Connecting lincolnshire and Yorkshire – image full text description