gsamaras - 4 months ago 28

C++ Question

I have N points in D dimensions, where let's say N is 1 million and D 1 hundred. All my points have binary coordinates, i.e. {0, 1}^D, and I am only interested in *speed*.

Currently my implementation uses

`std::vector<int>`

All related questions I found mention

`std::vector<char>`

`std::vector<bool>`

`std::bitset`

What's the appropriate data structure, when speed is of main concern, for binary data in C++?

I intend to populate my data structure with the binary data and then do a lot of contiguous searches (I mean that I don't really care for the i-th coordinate of a point, if I am accessing a point I will access all of its coordinates continuously). I will compute the

Answer

Locality of reference will likely be the driving force. So it's fairly obvious that you represent the `D`

coordinates of a single point as a contiguous bitvector. `std::bitset<D>`

would be a logical choice.

However, the next important thing to realize is that you see locality benefits easily up to 4KB. This means that you should not pick a single point and compare it against all other N-1 points. Instead, group points in sets of 4KB each, and compare those groups. Both ways are `O(N*N)`

, but the second will be much faster.

You may be able to beat `O(N*N)`

by use of the triangle inequality - `Hamming(a,b)+Hamming(b,c) >= Hamming (a,c)`

. I'm just wondering how. It probably depends on how you want your output. The naive output would be a N*N set of distances, and that's unavoidably `O(N*N)`

.