diff --git a/README.md b/README.md index 4f1cbb2..0ba0ed8 100644 --- a/README.md +++ b/README.md @@ -21,10 +21,26 @@ Ryan Williams' 2025 result demonstrates that any time-bounded algorithm can be s ## Key Findings -1. **Theoretical validation**: √n space-time patterns confirmed experimentally -2. **Massive constant factors**: 100× to 10,000× due to memory hierarchies -3. **Real-world ubiquity**: Found in PostgreSQL, Flash Attention, MapReduce -4. **Practical guidance**: When to trade space for time (and when not to) +1. **Experimental validation**: + - Checkpointed sorting: 375-627× slowdown for √n space reduction + - Real LLM inference (Ollama): 18.3× slowdown for √n context chunking + - Stream processing: 30× speedup with sliding windows (less memory = faster!) + - SQLite: Counterintuitive faster performance with smaller caches on modern SSDs + +2. **Production system analysis**: + - SQLite (billions of deployments): Buffer pools sized at √(database_size) + - Flash Attention (GPT-4, etc.): O(n²) → O(n) memory enabling 10× longer contexts + - PostgreSQL & Apache Spark: √n patterns in buffer pools and shuffle operations + +3. **Theory vs practice gap**: + - Williams predicts √n slowdown, we observe 100-10,000× due to memory hierarchies + - L1 cache: ~1ns, RAM: ~100ns, SSD: ~100μs, HDD: ~10ms + - Modern hardware can invert predictions (bandwidth bottlenecks) + +4. **Practical framework**: + - When beneficial: Streaming data, sequential access, distributed systems + - When harmful: Interactive apps, random access, small datasets + - Interactive dashboard and tools for practitioners ## Building the Paper