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Nice paper building on top of [the WebGraph framework](https://papers-gamma.link/paper/31) and [Chierichetti et al.](https://papers-gamma.link/paper/126) to compress graphs. ### Approximation guarantee I read: "our algorithm is inspired by a theoretical approach with provable guarantees on the final quality, and it is designed to directly optimize the resulting compression ratio.". I misunderstood initially, but the proposed algorithm actually does not have any provable approximation guarantee other than the $\log(n)$ one (which is also obtained by a random ordering of the nodes). Designing an algorithm with (a better) approximation guarantee for minimizing "MLogA", "MLogGapA" or "BiMLogA" seems to be a nice open problem. ### Objectives Is there any better objective than "MLogA", "MLogGapA" or "BiMLogA" to have a proxy of the compression obtained by the BV-framework? Is it possible to directly look for an ordering that minimizes the size of the output of BV compression algorithm?
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> I need to understand this part in clear way if that is possible please I see. I agree it is not perfectly clear, sorry about that. Can you try to understand it with the branch and bound [wikipedia page](https://en.wikipedia.org/wiki/Branch_and_bound), [the slides](https://drive.google.com/file/d/0B6cGK503Ibt0Qlg3bUVKRnFBTG8/view) and [the code](https://github.com/maxdan94/HkS)? If it is still not clear after that, please come back and I'll try to phrase a better explanation ASAP.
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