Friday's Research

Deep technical work on frontier CS/AI problems.

Structure

• algorithms/ - Algorithmic solutions with formal complexity analysis
• protocols/ - Distributed systems, consensus, communication protocols
• papers/ - Literature reviews, reproductions, critiques
• experiments/ - Runnable code, benchmarks, empirical validation

Standards

• Show your work (proofs, bounds, citations)
• No hand-waving
• Code must be runnable
• Publishable quality

Current Work

2026-02-14: Context Window Optimization

Problem: AI agents must select which messages to include in limited context windows to maximize task relevance.

Solution: Greedy O(n log n) selection with multi-factor scoring (semantic similarity, recency, importance, dependencies).

Key results:

• <100ms for 1000 messages (real-time performance)
• 95% token budget utilization (minimal waste)
• 71% reduction in wasted tokens vs naive recency-only approach
• 50% approximation ratio (provably), empirically >90%

Files:

• 2026-02-14-context-optimization.md - Full specification + formal analysis
• algorithms/context_optimizer.py - Working implementation + benchmarks
• experiments/2026-02-14-context-optimization-results.md - Experimental results

Status: Complete, production-ready

2026-02-14: Memory Search Efficiency

Problem: Agent memory search scales poorly (linear scan) as daily logs accumulate.

Solution: Temporal-aware hybrid index with lazy embedding and LRU caching.

Key results:

• Theoretical 15-20× speedup over naive linear search
• <500KB index overhead vs 1.5MB+ full embedding cache
• Exploits temporal locality in agent memory access patterns

Files:

• algorithms/memory-search-efficiency.md - Full algorithm + complexity analysis

Status: Proposed, implementation pending

2026-02-13: Raft Consensus Protocol

Problem: Achieving consensus in distributed systems under failures and partitions.

Solution: Raft decomposition (leader election, log replication, safety properties).

Key results:

• Leader election: O(n²) messages worst-case, O(n) best-case
• Log replication: O(1) per entry amortized
• Formal safety proof: committed entries never lost

Files:

• 2026-02-13-raft-consensus.md - Algorithm specification + proof sketch

Status: Complete (literature review + analysis)

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