https://github.com/bqi343/innerproductmax.jl
Data structures supporting fast maximum inner product queries in three dimensions. Final Project for MIT 6.8410 (Shape Analysis).
https://github.com/bqi343/innerproductmax.jl
julia
Last synced: 10 months ago
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Data structures supporting fast maximum inner product queries in three dimensions. Final Project for MIT 6.8410 (Shape Analysis).
- Host: GitHub
- URL: https://github.com/bqi343/innerproductmax.jl
- Owner: bqi343
- License: mit
- Created: 2023-03-22T05:30:06.000Z (over 3 years ago)
- Default Branch: main
- Last Pushed: 2023-04-01T21:45:07.000Z (about 3 years ago)
- Last Synced: 2025-03-27T07:49:52.082Z (over 1 year ago)
- Topics: julia
- Language: Julia
- Homepage:
- Size: 26.3 MB
- Stars: 0
- Watchers: 1
- Forks: 2
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- License: LICENSE
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README
# Inner Product Maximization in 3 Dimensions
## About
Four different data structures solving [this task](https://cstheory.stackexchange.com/questions/34503/maximizing-inner-product) with $d=3$.
## Usage
### Basic Usage
```julia
using GeometryBasics, InnerProductMax # this may take a while ...
const T = Float64
const P3 = Point3{T}
point_set = tetrahedron(T) # initialize a non-degenerate 3xn point set
display(point_set) # 3x5
hull = Hull(point_set) # construct 3D hull
ds = InnerProductMaxMine{T, PointLocationDsTreap}(hull) # initialize inner product maximization data structure
display(query_all(ds, vec_to_matrix(P3[P3(3, 1, 2), P3(-3, -1, -2)]))) # query max vector
# 3×2 Matrix{Float64}:
# 1.0 0.0
# 0.0 0.0
# 1.0 0.0
```
### Interactive Plot
This should open in a separate window after a while.
```julia
using InnerProductMax
const T = Float64
# point_set = tetrahedron(T)
point_set = unit_sphere(T, 10)
# plot_3d_hull_interactive(InnerProductMaxMine{T, PointLocationDsTreap}, point_set)
plot_point_location_interactive(InnerProductMaxMine{T, PointLocationDsTreap}, point_set)
```
`plot_3d_hull_interactive` displays only the polyhedron, whereas `plot_point_location_interactive` displays both the polyhedron and the planar subdivision (available when `InnerProductMaxMine` is used).
#### Troubleshooting
If you're having trouble seeing the plots or want a sanity check that `GLMakie` is working, try running the following code (e.g., by starting Julia from the Mac Terminal app and pasting in the lines):
```julia
# source: https://github.com/MakieOrg/Makie.jl/issues/797
using GLMakie
xy = rand(Point2f, 10)
colors = rand(10)
points_node = Observable(xy)
scene = scatter(points_node, color=colors)
```
Expected Output:
### Subclasses of `AbstractInnerProductMax{T}`
Listed from best to worst complexity.
| Subclass | Preprocessing Time | Preprocessing Memory | Query Time |
| --------------------------------------------- | ------------------ | -------------------- | ----------- |
| InnerProductMaxNaive{T} | $O(N)$ | $O(N)$ | $O(N)$ |
| InnerProductMaxMine{T,PointLocationDsTreap} | $O(N\log N)$ | $O(N\log N)$ | $O(\log N)$ |
| InnerProductMaxMine{T,PointLocationDsRB} | $O(N\log N)$ | $O(N)$ | $O(\log N)$ |
| InnerProductMaxNested{T} | $O(N)$ | $O(N)$ | $O(\log N)$ |
In practice, for a hull of size $N\approx 10^5$, `InnerProductMaxMine{T,PointLocationDsTreap}` is the fastest in terms of query time, while `InnerProductMaxMine{T,PointLocationDsRB}` has slightly lower preprocessing time and memory but slightly larger query time.
## Dev Instructions
Add these to `startup.jl`: `using Revise, ReTest, TestEnv`. Run these commands from the repo root to execute all tests:
```
julia --project
TestEnv.activate() do
include("test/InnerProductMaxTests.jl"); retest()
end
```
## Performance Tests
```
include("test/InnerProductMaxTests.jl"); retest("sphere_perf")
```
Results:
```
N Q Method Preproc Time (s) Preproc Memory (MB) Query Time (s)
0 1000 1000 Naive 0.000017 0.088208 0.002308
1 1000 1000 Mine 0.010655 8.234688 0.003923
2 2000 2000 Naive 0.000092 0.176208 0.008973
3 2000 2000 Mine 0.023383 17.890672 0.003160
4 5000 5000 Naive 0.000276 0.440208 0.046815
5 5000 5000 Mine 0.081375 48.884608 0.017122
6 10000 10000 Naive 0.000646 0.880208 0.204886
7 10000 10000 Mine 0.321766 102.224256 0.022775
8 20000 20000 Naive 0.001080 1.760208 0.712584
9 20000 20000 Mine 0.370499 210.870496 0.056952
10 50000 50000 Naive 0.003199 4.400208 4.347602
11 50000 50000 Mine 0.841139 562.539104 0.189053
12 100000 100000 Naive 0.008528 8.800208 29.408380
13 100000 100000 Mine 4.712876 1162.170496 0.430899
```
Red-black tree (memory is worse for some reason ...)
```
N Q Method Preproc Time (s) Preproc Memory (MB) Query Time (s)
0 1000 1000 Naive{Float64} 0.000030 0.088208 0.001731
1 1000 1000 Mine{Float64, InnerProductMax.PLRB.PointLocati... 0.836934 30.685142 0.002265
2 2000 2000 Naive{Float64} 0.000093 0.176208 0.008567
3 2000 2000 Mine{Float64, InnerProductMax.PLRB.PointLocati... 0.127989 43.213336 0.005933
4 5000 5000 Naive{Float64} 0.000293 0.440208 0.057106
5 5000 5000 Mine{Float64, InnerProductMax.PLRB.PointLocati... 0.294365 111.242704 0.017334
6 10000 10000 Naive{Float64} 0.000544 0.880208 0.184570
7 10000 10000 Mine{Float64, InnerProductMax.PLRB.PointLocati... 0.903501 233.486320 0.099521
8 20000 20000 Naive{Float64} 0.008901 1.760208 0.722730
9 20000 20000 Mine{Float64, InnerProductMax.PLRB.PointLocati... 1.334035 482.795608 0.110320
```
After some optimization:
```
N Q Method Preproc Time (s) Preproc Memory (MB) Query Time (s)
0 1000 1000 Naive{Float64} 0.000018 0.088208 0.002407
1 1000 1000 Mine{Float64, InnerProductMax.PLRB.PointLocati... 0.036450 7.696784 0.001469
2 2000 2000 Naive{Float64} 0.000068 0.176208 0.007784
3 2000 2000 Mine{Float64, InnerProductMax.PLRB.PointLocati... 0.169119 16.005184 0.017737
4 5000 5000 Naive{Float64} 0.000295 0.440208 0.060403
5 5000 5000 Mine{Float64, InnerProductMax.PLRB.PointLocati... 0.166669 40.568920 0.011874
6 10000 10000 Naive{Float64} 0.000654 0.880208 0.208089
7 10000 10000 Mine{Float64, InnerProductMax.PLRB.PointLocati... 0.263313 84.020904 0.019850
8 20000 20000 Naive{Float64} 0.000946 1.760208 0.854989
9 20000 20000 Mine{Float64, InnerProductMax.PLRB.PointLocati... 0.612379 161.643320 0.054820
10 50000 50000 Naive{Float64} 0.003221 4.400208 4.820060
11 50000 50000 Mine{Float64, InnerProductMax.PLRB.PointLocati... 1.845995 408.716920 0.180039
12 100000 100000 Naive{Float64} 0.007666 8.800208 21.956377
13 100000 100000 Mine{Float64, InnerProductMax.PLRB.PointLocati... 4.109249 820.536728 1.290055
```
Preprocessing time and memory are only slightly less than for treap. Perhaps the constant factor can be improved with more effort.
Note: We can significantly reduce the constant factor for queries using an optimization suggested in the paper.
```
N Q Method Preproc Time (s) Preproc Memory (MB) Query Time (s)
0 1000 1000 Naive{Float64} 0.000040 0.088208 0.001708
1 1000 1000 Mine{Float64, InnerProductMax.PLRB.PointLocati... 0.030870 7.476016 0.001962
2 2000 2000 Naive{Float64} 0.000072 0.176208 0.008648
3 2000 2000 Mine{Float64, InnerProductMax.PLRB.PointLocati... 0.062812 15.480224 0.002720
4 5000 5000 Naive{Float64} 0.000287 0.440208 0.053640
5 5000 5000 Mine{Float64, InnerProductMax.PLRB.PointLocati... 0.308152 39.286704 0.011566
6 10000 10000 Naive{Float64} 0.000798 0.880208 0.240438
7 10000 10000 Mine{Float64, InnerProductMax.PLRB.PointLocati... 0.362468 81.181088 0.023628
8 20000 20000 Naive{Float64} 0.001247 1.760208 0.788075
9 20000 20000 Mine{Float64, InnerProductMax.PLRB.PointLocati... 1.196662 156.532464 0.172948
10 50000 50000 Naive{Float64} 0.002310 4.400208 5.471993
11 50000 50000 Mine{Float64, InnerProductMax.PLRB.PointLocati... 2.251654 395.703808 0.237956
12 100000 100000 Naive{Float64} 0.001890 8.800208 21.455233
13 100000 100000 Mine{Float64, InnerProductMax.PLRB.PointLocati... 3.934218 793.702672 0.554677
```
Level Nesting:
```
N Q Method Preproc Time (s) Preproc Memory (MB) Query Time (s)
0 1000 1000 Naive{Float64} 0.123188 21.083010 0.001706
1 1000 1000 Nested{Float64} 2.606700 210.646009 0.295431
2 2000 2000 Naive{Float64} 0.000084 0.176208 0.009147
3 2000 2000 Nested{Float64} 1.308404 67.983136 0.170769
4 5000 5000 Naive{Float64} 0.000200 0.440208 0.059044
5 5000 5000 Nested{Float64} 3.226397 201.209808 0.727922
6 10000 10000 Naive{Float64} 0.000579 0.880208 0.194339
7 10000 10000 Nested{Float64} 7.278815 512.164288 1.641210
8 20000 20000 Naive{Float64} 0.001400 1.760208 0.828003
9 20000 20000 Nested{Float64} 14.881884 1451.676352 4.268223
```
## TODOs
- remove Dict from subhull? idk if that will be faster
- polish docs + performance tests
- generate more interesting point distributions?
- make visualization work for larger number of points?