EmptySpaceSearch 0.3.1

Empty Space Search

Empty Space Search (ESS)

ESS is a high-performance Python library that implements the Electrostatic Search Algorithm (ESA), a novel method for generating spatially diverse point distributions. It simulates electrostatic repulsive forces to "relax" new points into the empty spaces of a high-dimensional domain, making it ideal for sampling, coverage optimization, and exploratory data analysis.

Features

• Electrostatic Search Algorithm (ESA): Uses physics-inspired repulsive forces (Gaussian, Softened Inverse, etc.) to maximize the separation between points.
• Radius-Based Interactions (New in v0.3.0): Supports physical range searches (interacting with all neighbors within a radius) alongside standard k-NN, with automatic radius estimation for high-dimensional spaces.
• Repulsive Boundaries: Implements "soft walls" that exert restorative forces at domain edges, preventing the edge-clumping artifacts common in hard-clipped optimization.
• Scalable Architecture:
  • NumpyNN: Vectorized pure NumPy implementation with norm caching. Efficient for N < 5,000.
  • FaissHNSW: Wraps Faiss HNSW graphs for logarithmic scaling on large datasets (N > 50,000).
• High-Dimensional Metrics: Includes robust coverage metrics (Maximin, Clark-Evans Index, Sparse Grid Coverage) optimized for dimensions > 32D.
• Smart Initialization: Uses a vectorized "Best Candidate" sampling strategy to seed new batches in the most promising void regions.

Note: The library is designed to be compliant with modern Python 3.12+ standards.

Installation

The library can be installed directly from PyPI:

pip install EmptySpaceSearch

Alternatively, you can install the latest development version directly from GitHub:

pip install git+[https://github.com/mariolpantunes/ess.git](https://github.com/mariolpantunes/ess.git)

Requirements:

• Python >= 3.12
• numpy
• faiss-cpu

Usage

Basic Example

Generate 100 new points in a 2D space using the default settings (Auto-Radius + Repulsive Walls):

import numpy as np
import ess

# Define existing points (e.g., obstacles)
obstacles = np.array([[0.5, 0.5]]) 
bounds = np.array([[0, 1], [0, 1]])

# Generate 100 new points
# 'ess' returns the combined set (obstacles + new points)
result = ess.ess(obstacles, bounds, n=100, seed=42, border_strategy='repulsive')

print(f"Total points: {len(result)}")

Advanced Usage with Faiss & Radius Search

For large datasets, explicitly use the FaissHNSWFlatNN backend and the new physics-based radius mode:

import numpy as np
from ess import esa, FaissHNSWFlatNN

# 1000 existing points in 50 dimensions
dim = 50
obstacles = np.random.rand(1000, dim)
bounds = np.array([[0, 1]] * dim)

# Initialize HNSW Engine for speed
nn_engine = FaissHNSWFlatNN(dimension=dim, seed=42)

# Run ESA (returns ONLY the new points)
# search_mode='radius' activates the dense physical interaction model
new_points = esa(
    obstacles, 
    bounds, 
    n=500, 
    nn_instance=nn_engine,
    search_mode='radius',  # Use radius instead of k-NN
    radius=None,           # None = Auto-compute based on density
    batch_size=100, 
    epochs=256
)

Algorithms

ESA (Electrostatic Search Algorithm) treats existing points as fixed charged particles and new points as free moving charges.

1. k-NN Mode: Points are repelled by their nearest neighbors. Good for maintaining local uniformity.
2. Radius Mode (New): Points are repelled by all neighbors within a specific cutoff radius . This mimics real electrostatic fields and prevents "tunneling" in high-density regions.

Force Functions:

• softened_inverse: Standard electrostatic repulsion (Coulomb-like).
• gaussian: Smooth, short-range repulsion.
• linear: Simple linear drop-off (Hookean spring).
• cauchy: Heavy-tailed distribution for global separation.

Documentation

This library is documented using Google-style docstrings.

You can access the full documentation online here.

To generate the documentation locally using pdoc:

pdoc --math -d google -o docs src/ess \
    --logo assets/ess_logo.svg \
    --favicon assets/ess_logo.svg

Authors

• Mário Antunes - mariolpantunes

License

This project is licensed under the MIT License - see the LICENSE file for details.

MIT License

Copyright (c) 2025 Mário Antunes

Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.