To the first question: yes. The reference is here: https://ieeexplore.ieee.org/document/6494675/ …. There's also tricks for computing the Fourier transform on graph faster.
Thinking about garbage collection: is there any graph theory analog to the Fourier Transform? A new space derived from the objects-and-references space which enables asymptotically more efficient determination or update of liveness? Bloom filter mojo?
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I've wondered about this. I suspect non-deterministic GC could be a fruitful research program; it's really not a problem if a certain % of the space is wrongly marked as live at any given point, as long as the chance converges to 0 eventually
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The FT is the SVD of a Toeplitz matrix. Maybe if your incidence matrices had a specific structure there would be a transform for it (wavelets?). But I don't think there can be a general form for "all graphs" since the set of all arbitrary matrices includes the uncompressible ones
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Unless your graph is time variant, you can express it as a state space filter: https://ccrma.stanford.edu/~jos/fp/State_Space_Filters.html … Old school control sys folks use them a lot. Once you get your graph in a state space representation you can gauge its frequency response
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These are specifically time-varying. Discrete time, but all computers use discrete time so nbd.
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Like storing a couple of extra bits per object related to distance from root on previous trace? Sometimes set to unknown during freeing of parent to help save time on future traces? I haven't liked anything I've written yet enough to optimize it heavily.
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Spectral graph theory I guess, but I don't think that has much grip on digraphs yet.
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UObject base layout did this in the early days. Doesn’t scale well to inheritance, though, and automatic sequential prefetching by the CPU seems to help. Really the problem with Unreal GC isn’t the amortized overhead - like 0.1%, it’s the single-threaded pause time.
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