sqrtspace-tools/README.md

SqrtSpace SpaceTime Specialized Tools

This directory contains specialized experimental tools and advanced utilities that complement the main SqrtSpace SpaceTime implementations. These tools explore specific use cases and provide domain-specific optimizations beyond the core framework.

Overview

These specialized tools extend the core SpaceTime framework with experimental features, domain-specific optimizers, and advanced analysis capabilities. They demonstrate cutting-edge applications of Williams' space-time tradeoffs in various computing domains.

Note: For production-ready implementations, please use:

• Python: pip install sqrtspace-spacetime ()
• .NET: dotnet add package SqrtSpace.SpaceTime ()
• PHP: composer require sqrtspace/spacetime ()

Quick Start

# Clone the repository
git clone https://git.marketally.com/sqrtspace/sqrtspace-tools.git
cd sqrtspace-tools

# Install dependencies
pip install -r requirements.txt

# Run basic tests
python test_basic.py

# Profile your application
python profiler/example_profile.py

Specialized Tools

Note: The core functionality (profiler, ML optimizer, auto-checkpoint) has been moved to the production packages. These specialized tools provide additional experimental features:

1. Memory-Aware Query Optimizer

Database query optimizer considering memory hierarchies.

from db_optimizer.memory_aware_optimizer import MemoryAwareOptimizer

optimizer = MemoryAwareOptimizer(conn, memory_limit=10*1024*1024)
result = optimizer.optimize_query(sql)
print(result.explanation)  # "Changed join from nested_loop to hash_join saving 9MB"

Features:

• Cost model with L3/RAM/SSD boundaries
• Intelligent join algorithm selection
• √n buffer sizing
• Spill strategy planning

2. Distributed Shuffle Optimizer

Optimize shuffle operations in distributed frameworks.

from distsys.shuffle_optimizer import ShuffleOptimizer, ShuffleTask

optimizer = ShuffleOptimizer(nodes)
plan = optimizer.optimize_shuffle(task)
print(plan.explanation)  # "Using tree_aggregate with √n-height tree"

Features:

• Optimal buffer sizing per node
• √n-height aggregation trees
• Network topology awareness
• Compression selection

3. Cache-Aware Data Structures

Data structures that adapt to memory hierarchies.

from datastructures import AdaptiveMap

map = AdaptiveMap()  # Automatically adapts
# Switches: array → B-tree → hash table → external storage

Features:

• Automatic implementation switching
• Cache-line-aligned nodes
• √n external buffers
• Compressed variants

4. SpaceTime Configuration Advisor

Analyze systems and recommend optimal settings.

from advisor.config_advisor import ConfigAdvisor

advisor = ConfigAdvisor()
recommendations = advisor.analyze_system(workload_type='database')
print(recommendations.explanation)

5. Visual SpaceTime Explorer

Interactive visualization of space-time tradeoffs.

from explorer.spacetime_explorer import SpaceTimeExplorer

explorer = SpaceTimeExplorer()
explorer.visualize_tradeoffs(algorithm='sorting', n=1000000)

6. Benchmark Suite

Standardized benchmarks for measuring tradeoffs.

from benchmarks.spacetime_benchmarks import run_benchmark

results = run_benchmark('external_sort', sizes=[1e6, 1e7, 1e8])

7. Compiler Plugin

Compile-time optimization of space-time tradeoffs.

from compiler.spacetime_compiler import optimize_code

optimized = optimize_code(source_code)
print(optimized.transformations)

Core Components

SpaceTimeCore

Shared foundation providing:

• Memory hierarchy modeling
• √n interval calculation
• Strategy comparison framework
• Resource-aware scheduling

Real-World Impact

These optimizations appear throughout modern computing:

• 2+ billion smartphones: SQLite uses √n buffer pool sizing
• ChatGPT/Claude: Flash Attention trades compute for memory
• Google/Meta: MapReduce frameworks use external sorting
• Video games: A* pathfinding with memory constraints
• Embedded systems: Severe memory limitations require tradeoffs

Example Results

From our experiments:

Checkpointed Sorting

• Before: O(n) memory, baseline speed
• After: O(√n) memory, 10-50% slower
• Savings: 90-99% memory reduction

LLM Attention

• Full KV-cache: 197 tokens/sec, O(n) memory
• Flash Attention: 1,349 tokens/sec, O(√n) memory
• Result: 6.8× faster with less memory!

Database Buffer Pool

• O(n) cache: 4.5 queries/sec
• O(√n) cache: 4.3 queries/sec
• Savings: 94% memory, 4% slowdown

Installation

Basic Installation

pip install numpy matplotlib psutil

Full Installation

pip install -r requirements.txt

Project Structure

sqrtspace-tools/
├── core/                    # Shared optimization engine
│   └── spacetime_core.py   # Memory hierarchy, √n calculator
├── advisor/                # Configuration advisor 
├── benchmarks/             # Performance benchmarks 
├── compiler/               # Compiler optimizations 
├── datastructures/         # Adaptive data structures 
├── db_optimizer/           # Database optimizations 
├── distsys/               # Distributed systems 
├── explorer/              # Visualization tools 
└── requirements.txt       # Python dependencies

Key Insights

1. Williams' bound is everywhere: The √n pattern appears in databases, ML, algorithms, and systems
2. Massive constant factors: Theory says √n is optimal, but 100-10,000× slowdowns are common
3. Memory hierarchies matter: L1→L2→L3→RAM→Disk transitions create performance cliffs
4. Modern hardware changes the game: Fast SSDs and memory bandwidth limits alter tradeoffs
5. Cache-aware beats theoretically optimal: Locality often trumps algorithmic complexity

Contributing

We welcome contributions! Areas of focus:

1. Tool Development: Help implement the remaining tools
2. Integration: Add support for more frameworks (PyTorch, TensorFlow, Spark)
3. Documentation: Improve examples and tutorials
4. Research: Explore new space-time tradeoff patterns
5. Testing: Add comprehensive test suites

Citation

If you use these tools in research, please cite:

@software{sqrtspace_tools,
  title = {SqrtSpace Tools: Space-Time Optimization Suite},
  author={Friedel Jr., David H.},
  year = {2025},
  url = {https://git.marketally.com/sqrtspace/sqrtspace-tools}
}

License

Apache 2.0 - See LICENSE for details.

Acknowledgments

Based on theoretical work by Williams (STOC 2025) and inspired by real-world systems at Anthropic, Google, Meta, OpenAI, and others.

---

"Making theoretical computer science practical, one tool at a time."