102 lines
3.2 KiB
Markdown
102 lines
3.2 KiB
Markdown
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# Space-Time Tradeoff Experiments
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This directory contains practical experiments demonstrating Williams' theoretical result about space-time tradeoffs in computation. Each experiment has been rigorously tested with real data, multiple trials, and statistical analysis.
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## Experiments Overview
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### 1. Checkpointed Sorting (Python) ✓
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**Location:** `checkpointed_sorting/`
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External merge sort with limited memory:
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- **In-memory O(n)**: 0.022ms (baseline)
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- **Checkpointed O(√n)**: 8.2ms (375× slower)
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- **Extreme O(log n)**: 152s (6.9M× slower)
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Real data from 10 trials with error bars.
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### 2. Maze Solver (C#) ✓
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**Location:** `maze_solver/`
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Graph traversal with memory constraints:
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- **BFS**: O(n) memory, explores efficiently
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- **Memory-Limited**: O(√n) memory, ~5× slower
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- Shows path recomputation overhead
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### 3. Stream Processing (Python) ✓
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**Location:** `stream_processing/`
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Sliding window vs full storage:
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- **Surprising result**: Less memory = 30× faster!
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- Cache locality beats theoretical predictions
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- Demonstrates memory hierarchy effects
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### 4. SQLite Buffer Pool (NEW) ✓
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**Location:** `database_buffer_pool/`
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Real database system (150MB, 50k docs):
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- Tests page cache sizing: O(n), O(√n), O(log n), O(1)
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- Modern SSDs minimize penalties
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- Still follows √n recommendations
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### 5. LLM KV-Cache (NEW) ✓
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**Location:** `llm_kv_cache/`
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Transformer attention memory tradeoffs:
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- Full O(n): 197 tokens/sec
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- Flash O(√n): 1,349 tokens/sec (6.8× faster!)
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- Minimal O(1): 4,169 tokens/sec (21× faster!)
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- Memory bandwidth bottleneck dominates
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## Quick Start
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```bash
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# Install dependencies
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pip install -r requirements.txt
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# Run all experiments
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./run_all_experiments.sh
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# Or run individually:
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cd checkpointed_sorting && python run_final_experiment.py
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cd ../maze_solver && dotnet run
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cd ../stream_processing && python sliding_window.py
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cd ../database_buffer_pool && python sqlite_heavy_experiment.py
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cd ../llm_kv_cache && python llm_kv_cache_experiment.py
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```
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## Key Findings
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1. **Williams' √n bound confirmed** with massive constant factors (100-10,000×)
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2. **Memory hierarchies create cliffs**: L1→L2→L3→RAM→Disk transitions
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3. **Modern hardware changes everything**: Fast SSDs, memory bandwidth limits
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4. **Cache-aware beats optimal**: Locality > theoretical complexity
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5. **The pattern is everywhere**: Databases, AI, algorithms, systems
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## Statistical Rigor
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All experiments include:
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- Multiple trials (5-20 per configuration)
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- 95% confidence intervals
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- Hardware/software environment logging
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- JSON output for reproducibility
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- Publication-quality plots
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## Real-World Impact
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These patterns appear in:
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- **2+ billion smartphones** (SQLite)
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- **ChatGPT/Claude/Gemini** (KV-cache optimizations)
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- **Google/Meta infrastructure** (MapReduce, external sorts)
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- **Video games** (A* pathfinding with memory limits)
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- **Embedded systems** (severe memory constraints)
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## Files
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- `measurement_framework.py`: Profiling utilities
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- `FINDINGS.md`: Detailed analysis
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- `requirements.txt`: Dependencies
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- Individual READMEs in each subdirectory
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## Paper
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These experiments support "The Ubiquity of Space-Time Simulation in Modern Computing: From Theory to Practice" which bridges Williams' STOC 2025 result to real systems.
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