Approximate Subset Sum
Find fast approximate solutions for the subset sum problem.
Installation
pip install approx_subsetsum
Usage
Given an integer numpy array samples, this function tries to find a subset of samples, that has a sum close to a given capacity.
import numpy as np
from approx_subsetsum import subsetsum
samples = np.array([1, 2, 3, 4, 5])
capacity = 7
indices = subsetsum(samples, capacity, timeout=10.0, allow_higher=100)
solution = samples[indices]
if np.sum(solution) == capacity:
print('found solution')
else:
print('solution is off by', abs(np.sum(solution) - capacity))
Parameters
samples: The input array of integers. Fastest if given as numpy array (no copy). Otherwise the data will be copied.capacity: The target sum as integer. High capacities can lead to high memory usage and runtime.timeout: The maximum runtime in seconds. If the algorithm does not find a solution within this time, it throws aapprox_subsetsum.TimeoutError.allow_higher: If set to a positive integer, the algorithm will also try to find a solution higher thancapacity(up tocapacity + allow_higher). Note that settingallow_higherto a large value can hurt performance.
Performance
The algorithm is not well optimized, but at least implemented in C++.
For the following measurements, a script similar to the following code snippet was executed:
import numpy as np
from approx_subsetsum import subsetsum
def bench(n_samples, capacity):
samples = np.random.randint(1, 1000000, n_samples)
subsetsum(samples, capacity, timeout=10.0)
The plot shows the runtime depending on the number of samples and the capacity.
The following table shows an overview of the runtimes. Of course, this depends on many things but can be used to get an idea of the performance.
| #samples | capacity | runtime |
|---|---|---|
| 1000 | 10000 | 0.000 secs |
| 10000 | 10000 | 0.001 secs |
| 100000 | 10000 | 0.006 secs |
| 1000000 | 10000 | 0.061 secs |
| 1000 | 100000 | 0.004 secs |
| 10000 | 100000 | 0.057 secs |
| 100000 | 100000 | 0.569 secs |
| 1000000 | 100000 | 5.887 secs |
| 1000 | 1000000 | 0.623 secs |
| 10000 | 1000000 | 6.093 secs |
| 100000 | 1000000 | >60 secs |
| 1000000 | 1000000 | >60 secs |
1 maintainer
Metadata
1 maintainer
Release files for approx-subsetsum 0.2.4
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Transparency logRelease files / approx_subsetsum-0.2.4-cp310-cp310-macosx_11_0_arm64.whl
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