> In finance, for example, there may be situations in currency or options trading where buying and selling in one sequence is more profitable than taking a different path, and these can be modeled using negative weights as long as the search algorithm is fast enough.
This is a non-contrived example. You could do this as a mini-project where you scrape various foreign exchange or cryptocurrency data, and try to find some arbitrage opportunities by running these shortest path algorithms.
To try to restate that. Someone owns currency A then buys B which is a cost, but it has a good exchange rate with currency C and C has a good exchange rate with A. So the B-C-A move yields a profit which would be representative as a negative weight. Is that right?
Yes, if trading BCA results in a profit, either BC or CA has negative weight. Negative weight here just means you can sell a currency more than its cost basis, and or buy a currency for cheaper than its cost basis.
Though with arbitrage, you typically want to find a cycle like BCAB so you have more of the initial currency you started off with.
This is a non-contrived example. You could do this as a mini-project where you scrape various foreign exchange or cryptocurrency data, and try to find some arbitrage opportunities by running these shortest path algorithms.