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Do algorithmic trading platforms typically have live-data access to stock data?
Algorithmic trading doesn't necessarily require live feeds. It is a very generic term describing trading based on the decisions made by a machine and not a person. One very prominent type of algo-trading is "high frequency trading". For HFT to be effective, not only do you need live feeds (which are provided by the exchanges electronically), you need them before others get them. That's why HFT traders put their machines as close as possible (physically) to the exchange data centers, sometimes even renting racks at the same datacenters from the exchanges themselves.