Local vs regional road connections

[jimrtex]

Thanks.

I'll be on the lookout for a situation that takes undue advantage of a surrounded fragment. In the meantime think about the situation where a township has two sizable fragments of roughly equal population, one of which is wholly surrounded by a city but the other sits on the perimeter of the same city. Those two parts both get their services from the same unit of government, the township, and form a clear community of interest based on that township. Shouldn't there be an incentive to keep the two parts in the same district? Compare that to the case where the same two fragments aren't fully surrounded and there is an incentive to keep them whole.

Prairie Township, Franklin County, Ohio is an example.

[jimrtex]

Yeah, but I fail to see the need for a pseudo node. The shortest path involves highway cuts, pseudo node or not. You have not persuaded me yet, what purpose it serves that somehow changes something.

I need a representation for geographic data. Suppose you were putting together a spreadsheet to help you balance populations for districts in a state. You might put one county on each row of the spreadsheet and one district on each column. At the intersection of the county row and district column you would but the population of the county. You could then sum the column to get the district population.

Minus information about the neighbors those cells with populations in them are nodes. That is they are a specific point (cell) that has information about the population and the assigned district.

Now suppose you decide to split the population of a county between two districts. In the spreadsheet you would fill population into a new cell for that county in a different column and deduct that population from the original cell. You have created a new node for that new information about the chopped county.

The only thing I have added for my nodes that wasn't part of the spreadsheet example is information about the neighbors. In my examples I display that neighbor information graphically in the form of links. It doesn't change the underlying need to create a new node to hold the split population from the fragment. It does facilitate visualizing where the links now fall after the chop.

I use sumif() to calculate each district's population. I place each unit (county or block) in a row, and then in one column insert the district number. If a unit needs to be divided, I split it into multiple rows.

[jimrtex]

The underlined sentence I can answer directly. I'll give thought to the other parts.

Definition: Node. A node is a reference point for a geographic unit. For a political unit the node is the primary place of government for that unit.

The node is a specific point not a jurisdiction. For a county it is the place where the county government meets. A couple of years ago I tried to use the whole county seat, but I ran into problems when chops took a bite out of the seat and I tried to score plans with those chops. From a software perspective a single point is preferred to a polygonal shape as well.

Government buildings will be on roads so there is always a clear definition of a local path between two nodes. Regional paths can only use state and federal highways. Government buildings may not directly be on a state highway, so I need to place the seat of government on some state or federal highway to create a path. If there are two regional paths between a pair of county nodes then I need to know the reference point to determine which regional path is the shortest connecting path in case there are chops of that county. I doubt the ambiguity of lengths comes up much if at all, but the software still needs a reference point for measurement.

What if a city hall is not within the corporate limits?

[jimrtex]

Actually if I've written my definition correctly, then the fragment you would like to use is an isolated fragment, in that it has no connections to other units, at most a local connection to other fragments in the chopped unit. That leads to rules that favor your preferred chop.

Definition: Isolated County. An isolated county is a county or equivalent that has no regional connections. Example: Pitkin county, CO.
  
Item: An isolated county is connected to a unit if there is a local connection to the unit.

Item: An isolated county fragment that has no regional connections to adjacent units in other counties in the same district is connected to a unit or fragment across county lines if there is a local connection to the unit.

The underlined narrowly defines the connections for your preferred chops. Without the underlined it would treat all isolated fragments the same whether or not there is a regional link to the rest of the district. Without the underlined it is simpler and either way it accommodates your preference. Any thoughts?

Oh, and I do like your signature. What's the source?

The map came from here. I found the page doing a search for "new york topographic maps".