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I’m using “Internet Download Manager”. It has the ability to resume a download from an earlier paused point. Other download managers, such as Firefox’s also offer this ability. How do these algorithms work in general? How does they normally keep track of where they’ve left off, and allow servers to know form where to resume?
There is no “algorithm”.
Look at RFC 2616, which covers HTTP/1.1, for the various range support it has; this is how a client program can tell the server to skip a number of [mega]bytes and thus “resume” the download where it left off. However, servers may ignore Range Retrieval Requests and thereby thwart/prohibit resuming downloads.
Remembering where to resume is left up to the client, but is trivially stored as a “number of bytes already downloaded” field somewhere.