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Is there an algorithm faster than topological sort or DFSto handle time series of edges?

(1) at time t = 0, there is one node.

(2) at each time t > 0, an edge comes along. At least one of the edge's endpoints was added into the graph before t.

I want to detect at each time t if there is a directed cycle.

I really want to take advantage of the input being a time series. But the algorithms I know all deal with static graph.

A good reference that is unlikely to be a broken link: wiki

Leedehai
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