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Davidrxyang / raines-2024-line-addition-problem

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rethink efficiency #70

Closed Davidrxyang closed 2 months ago

Davidrxyang commented 3 months ago

network efficiency should be total route efficiency * total cost, not total route efficiency / total cost.

  1. the most efficient hypothetical route between two stations is a direct connection because it is the simplest, therefore a "better" route efficiency should be a smaller route efficiency.

  2. for two networks with the same route efficiency, if one has greater total construction cost, then it is worse.

  3. we should be trying to minimize network efficiency: smaller total route efficiency is better, and smaller cost is better, so the two variables move in the same direction, hence it makes sense to have efficiency * cost.

  4. we need to account for the fact that starting a brand new line must cost a lot more than taking a line that is already in the process of being constructed and extending it. Imagine two networks with completely different designs but the same exact total geographical distance, the network with more lines must be more expensive. If this isn't clear, imagine two networks, but one network is a fully connected graph while the other network is a graph with many disconnected components - the multi-component graph network must have a higher construction cost.

Davidrxyang commented 3 months ago

renamed "route efficiency" to route complexity