SqrtSpace SpaceTime for Python

Memory-efficient algorithms and data structures for Python using Williams' √n space-time tradeoffs.

Paper Repository: github.com/sqrtspace/sqrtspace-paper

Installation

pip install sqrtspace-spacetime

For ML features:

pip install sqrtspace-spacetime[ml]

For all features:

pip install sqrtspace-spacetime[all]

Core Concepts

SpaceTime implements theoretical computer science results showing that many algorithms can achieve better memory usage by accepting slightly slower runtime. The key insight is using √n memory instead of n memory, where n is the input size.

Key Features

• Memory-Efficient Collections: Arrays and dictionaries that automatically spill to disk
• External Algorithms: Sort and group large datasets using minimal memory
• Streaming Operations: Process files larger than RAM with elegant API
• Auto-Checkpointing: Resume long computations from where they left off
• Memory Profiling: Identify optimization opportunities in your code
• ML Optimizations: Reduce neural network training memory by up to 90%

Quick Start

Basic Usage

from sqrtspace_spacetime import SpaceTimeArray, external_sort, Stream

# Memory-efficient array that spills to disk
array = SpaceTimeArray(threshold=10000)
for i in range(1000000):
    array.append(i)

# Sort large datasets with minimal memory
huge_list = list(range(10000000, 0, -1))
sorted_data = external_sort(huge_list)  # Uses only √n memory

# Stream processing
Stream.from_csv('huge_file.csv') \
    .filter(lambda row: row['value'] > 100) \
    .map(lambda row: row['value'] * 1.1) \
    .group_by(lambda row: row['category']) \
    .to_csv('processed.csv')

Examples

Basic Examples

See examples/basic_usage.py for comprehensive examples of:

• SpaceTimeArray and SpaceTimeDict usage
• External sorting and grouping
• Stream processing
• Memory profiling
• Auto-checkpointing

FastAPI Web Application

Check out examples/fastapi-app/ for a production-ready web application featuring:

• Streaming endpoints for large datasets
• Server-Sent Events (SSE) for real-time data
• Memory-efficient CSV exports
• Checkpointed background tasks
• ML model serving with memory constraints

See the FastAPI example README for detailed documentation.

Machine Learning Pipeline

Explore examples/ml-pipeline/ for ML-specific patterns:

• Training models on datasets larger than RAM
• Memory-efficient feature extraction
• Checkpointed training loops
• Streaming predictions
• Integration with PyTorch and TensorFlow

See the ML Pipeline README for complete documentation.

Memory-Efficient Collections

from sqrtspace_spacetime import SpaceTimeArray, SpaceTimeDict

# Array that automatically manages memory
array = SpaceTimeArray(threshold=1000)  # Keep 1000 items in memory
for i in range(1000000):
    array.append(f"item_{i}")

# Dictionary with LRU eviction to disk
cache = SpaceTimeDict(threshold=10000)
for key, value in huge_dataset:
    cache[key] = expensive_computation(value)

External Algorithms

from sqrtspace_spacetime import external_sort, external_groupby

# Sort 100M items using only ~10K memory
data = list(range(100_000_000, 0, -1))
sorted_data = external_sort(data)

# Group by with aggregation
sales = [
    {'store': 'A', 'amount': 100},
    {'store': 'B', 'amount': 200},
    # ... millions more
]

by_store = external_groupby(
    sales,
    key_func=lambda x: x['store']
)

# Aggregate with minimal memory
from sqrtspace_spacetime.algorithms import groupby_sum
totals = groupby_sum(
    sales,
    key_func=lambda x: x['store'],
    value_func=lambda x: x['amount']
)

Streaming Operations

from sqrtspace_spacetime import Stream

# Process large files efficiently
stream = Stream.from_csv('sales_2023.csv')
    .filter(lambda row: row['amount'] > 0)
    .map(lambda row: {
        'month': row['date'][:7],
        'amount': float(row['amount'])
    })
    .group_by(lambda row: row['month'])
    .to_csv('monthly_summary.csv')

# Chain operations
top_products = Stream.from_jsonl('products.jsonl') \
    .filter(lambda p: p['in_stock']) \
    .sort(key=lambda p: p['revenue'], reverse=True) \
    .take(100) \
    .collect()

Auto-Checkpointing

from sqrtspace_spacetime.checkpoint import auto_checkpoint

@auto_checkpoint(total_iterations=1000000)
def process_large_dataset(data):
    results = []
    for i, item in enumerate(data):
        # Process item
        result = expensive_computation(item)
        results.append(result)
        
        # Yield state for checkpointing
        yield {'i': i, 'results': results}
    
    return results

# Automatically resumes from checkpoint if interrupted
results = process_large_dataset(huge_dataset)

Memory Profiling

from sqrtspace_spacetime.profiler import profile, profile_memory

@profile(output_file="profile.json")
def my_algorithm(data):
    # Process data
    return results

# Get detailed memory analysis
result, report = my_algorithm(data)
print(report.summary)

# Simple memory tracking
@profile_memory(threshold_mb=100)
def memory_heavy_function():
    # Alerts if memory usage exceeds threshold
    large_list = list(range(10000000))
    return sum(large_list)

ML Memory Optimization

from sqrtspace_spacetime.ml import MLMemoryOptimizer
import torch.nn as nn

# Analyze model memory usage
model = nn.Sequential(
    nn.Linear(784, 256),
    nn.ReLU(),
    nn.Linear(256, 128),
    nn.ReLU(),
    nn.Linear(128, 10)
)

optimizer = MLMemoryOptimizer()
profile = optimizer.analyze_model(model, input_shape=(784,), batch_size=32)

# Get optimization plan
plan = optimizer.optimize(profile, target_batch_size=128)
print(plan.explanation)

# Apply optimizations
config = optimizer.get_training_config(plan, profile)

Advanced Features

Memory Pressure Handling

from sqrtspace_spacetime.memory import MemoryMonitor, LoggingHandler

# Monitor memory pressure
monitor = MemoryMonitor()
monitor.add_handler(LoggingHandler())

# Your arrays automatically respond to memory pressure
array = SpaceTimeArray()
# Arrays spill to disk when memory is low

Configuration

from sqrtspace_spacetime import SpaceTimeConfig

# Global configuration
SpaceTimeConfig.set_defaults(
    memory_limit=2 * 1024**3,  # 2GB
    chunk_strategy='sqrt_n',
    compression='gzip',
    external_storage_path='/fast/ssd/temp'
)

Parallel Processing

from sqrtspace_spacetime.batch import BatchProcessor

processor = BatchProcessor(
    memory_threshold=0.8,
    checkpoint_enabled=True
)

# Process in memory-efficient batches
result = processor.process(
    huge_list,
    lambda batch: [transform(item) for item in batch]
)

print(f"Processed {result.get_success_count()} items")

Real-World Examples

Processing Large CSV Files

from sqrtspace_spacetime import Stream
from sqrtspace_spacetime.profiler import profile_memory

@profile_memory(threshold_mb=500)
def analyze_sales_data(filename):
    # Stream process to stay under memory limit
    return Stream.from_csv(filename) \
        .filter(lambda row: row['status'] == 'completed') \
        .map(lambda row: {
            'product': row['product_id'],
            'revenue': float(row['price']) * int(row['quantity'])
        }) \
        .group_by(lambda row: row['product']) \
        .sort(key=lambda group: sum(r['revenue'] for r in group[1]), reverse=True) \
        .take(10) \
        .collect()

top_products = analyze_sales_data('sales_2023.csv')

Training Large Neural Networks

from sqrtspace_spacetime.ml import MLMemoryOptimizer, GradientCheckpointer
import torch.nn as nn

# Memory-efficient training
def train_large_model(model, train_loader, epochs=10):
    # Analyze memory requirements
    optimizer = MLMemoryOptimizer()
    profile = optimizer.analyze_model(model, input_shape=(3, 224, 224), batch_size=32)
    
    # Get optimization plan
    plan = optimizer.optimize(profile, target_batch_size=128)
    
    # Apply gradient checkpointing
    checkpointer = GradientCheckpointer()
    model = checkpointer.apply_checkpointing(model, plan.checkpoint_layers)
    
    # Train with optimized settings
    for epoch in range(epochs):
        for batch in train_loader:
            # Training loop with automatic memory management
            pass

Data Pipeline with Checkpoints

from sqrtspace_spacetime import Stream
from sqrtspace_spacetime.checkpoint import auto_checkpoint

@auto_checkpoint(total_iterations=1000000)
def process_user_events(event_file):
    processed = 0
    
    for event in Stream.from_jsonl(event_file):
        # Complex processing
        user_profile = enhance_profile(event)
        recommendations = generate_recommendations(user_profile)
        
        save_to_database(recommendations)
        processed += 1
        
        # Checkpoint state
        yield {'processed': processed, 'last_event': event['id']}
    
    return processed

# Automatically resumes if interrupted
total = process_user_events('events.jsonl')

Performance Benchmarks

Operation	Standard Python	SpaceTime	Memory Reduction	Time Overhead
Sort 10M integers	400MB	20MB	95%	40%
Process 1GB CSV	1GB	32MB	97%	20%
Group by on 1M rows	200MB	14MB	93%	30%
Neural network training	8GB	2GB	75%	15%

API Reference

Collections

• SpaceTimeArray: Memory-efficient list with disk spillover
• SpaceTimeDict: Memory-efficient dictionary with LRU eviction

Algorithms

• external_sort(): Sort large datasets with √n memory
• external_groupby(): Group large datasets with √n memory
• external_join(): Join large datasets efficiently

Streaming

• Stream: Lazy evaluation stream processing
• FileStream: Stream lines from files
• CSVStream: Stream CSV rows
• JSONLStream: Stream JSON Lines

Memory Management

• MemoryMonitor: Monitor memory pressure
• MemoryPressureHandler: Custom pressure handlers

Checkpointing

• @auto_checkpoint: Automatic checkpointing decorator
• CheckpointManager: Manual checkpoint control

ML Optimization

• MLMemoryOptimizer: Analyze and optimize models
• GradientCheckpointer: Apply gradient checkpointing

Profiling

• @profile: Full profiling decorator
• @profile_memory: Memory-only profiling
• SpaceTimeProfiler: Programmatic profiling

Contributing

We welcome contributions! Please see our Contributing Guide for details.

License

Apache License 2.0. See LICENSE for details.

Citation

If you use SpaceTime in your research, please cite:

@software{sqrtspace_spacetime,
  title = {SqrtSpace SpaceTime: Memory-Efficient Python Library},
  author={Friedel Jr., David H.},
  year = {2025},
  url = {https://github.com/sqrtspace/sqrtspace-python}
}

Links

• Documentation
• PyPI Package
• GitHub Repository
• Issue Tracker