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Data Structures Part 3: Arrays of Arrays

• zawerf 7y ago
  There was a really interesting post on this topic recently where you have a circular array of circular arrays of size sqrt(n). [1] The result is you can do O(1) access, O(sqrt(N)) insert and delete at arbitrary indices, and O(1) insert at head and tail. In terms of big O this is strictly better than: - arrays: O(1) access, O(N) insert/delete in middle, O(1) insert/delete at tail. - circular arrays: O(1) access, O(N) insert/delete in middle, O(1) insert/delete at head and tail. - fixed page size chunked circular arrays such as the c++ implementation of std:deque which is still O(N) for insert and delete. [2] [1] https://news.ycombinator.com/item?id=20872696 https://news.ycombinator.com/item?id=20872696 [2] https://stackoverflow.com/questions/6292332/what-really-is-a-deque-in-stl https://stackoverflow.com/questions/6292332/what-really-is-a...
  • jbapple 7y ago
    Assuming you ignore the constant. And if you're willing to ignore the constant, you can get O(c) access, O(N^(1/c)) insert and delete at arbitrary indices, and O(c) insert at head and tail, for any constant c. The trick is to make the array into a B-tree of width N^(1/c) and depth c. Note that the insert/delete time is amortized: the worst-case time is O(cN^(1/c)).
    • zawerf 7y ago
      Yea someone else also mentioned that generalization (called a tiered vector) in that thread: https://news.ycombinator.com/item?id=20873110 https://news.ycombinator.com/item?id=20873110
  • htfy96 7y ago
    It's actually a simplified 2-layer skip list implementation.
• lpghatguy 7y ago
  A lot of the trade-offs in picking a fixed size array versus a heap allocated array can be solved with a container that supports small vector optimization! You see this in C++'s std::string type, which leads some people to use it for storing binary data. [1] I'm not sure what common STL-ish implementations of the idea exist. In Rust, there's SmallVec, which has configurable storage backing and spills onto the heap when there are too many elements. [2] [1] https://stackoverflow.com/a/21710033/802794 https://stackoverflow.com/a/21710033/802794 [2] https://docs.rs/smallvec/0.6.10/smallvec/struct.SmallVec.html https://docs.rs/smallvec/0.6.10/smallvec/struct.SmallVec.htm...
  • deleted 7y ago
    [deleted]
  • bullen 7y ago
    What is the difference between this "small" vector and a vector?
    • QuadDamaged 7y ago
      `SmallVec` allocates a contiguous array in the struct holding the vector itself (so it can be located on the stack), then if the capacity is insufficent, fallbacks to a heap-allocated `Vec` equivalent. The `Vec` struct contains the capacity and used length integers, as well as a pointer to the heap-allocated storage.
    • PixelOfDeath 7y ago
      The small vector class contains a static array of a few bytes. And as long as your data fits in it, no extra heap allocation is needed. A vector always does heap allocation, even if you only use a few bytes.
      • Vogtinator 7y ago
        Sounds like small string optimization (SSO), which is common in C++.
      • 7y ago
• bullen 7y ago
  I'm implementing cache friendly iteration on my open-source multiplayer server even though it is written in Java because I'm going to need it for my C+ client later. So I did thread safe compacting from the end which works fine, but now I want to implement 8-neighbor sending on an array and that can easily be done with fixed over-sized boxes. My question now is: if I use the trick Niklas calls “array with holes” in part 1, will each hole larger than the cache frame result in a cache miss?
  • corysama 7y ago
    It doesn’t sound like you are mentally modeling cache misses correctly. Any access to any array (dense or holey) that isn’t already in cache will result in a miss. A goal is to minimize misses by taking advantage of locality and prefetching. Let’s assume you have an array of objects that are small enough that 4 can fit in a cache line. You take advantage of locality by densely packing them into an array so that you can process 4 adjacent (and aligned) items for the price of only 1 cache miss. The array with holes can reduce your utilization by mixing live and dead data in a single cache line. Worst case would be 1 live item followed by a hole that means the next 3 in the cache line are dead bytes. That cache line only buys you 1 item to process. But, if the hole continues for several more cache lines it’s shouldn’t matter because you should have a means in place to skip all of that dead data and go straight to the next live item. You take advantage of prefetching by processing your array linearly from start to finish so that the CPU will notice and start fetching cache lines further down the array before you even try to access them. Arrays with holes can mess this up by making your access pattern irregular. If your array is very sparse you will be accessing cache lines without a repeating pattern and the CPU won’t be able to figure out how to help. But, the goal is for your array to be fairly dense (or at least reasonably defragmented) so that you end up accessing long, continuous spans of cache lines that make the prefetcher happy. At a minimum, the goal is to do better than most multilevel/tree-based data structures. Check out the writings and presentations of Martin Thompson (“mechanical sympathy” guy). He has made a career of getting good performance out of Java by coding it in the style of embedded-device C programs.
    • bullen 7y ago
• known 7y ago
  Learning arrays of arrays from Perl is easy https://perldoc.perl.org/perldsc.html https://perldoc.perl.org/perldsc.html