AI and the World's Hard Problems · Theoretical computer science · arXiv · 2026-10-22
Parallel AI Agent Collaboration as Graph-Structured Distributed Block Optimization
Parallel AI agents can produce useful local edits that degrade a shared solution when combined. The paper models this coordination problem as discrete block optimization with an exactly evaluable objective and a known dependency graph, where independent sets certify compatible edits whose verified gains add exactly, and proves that an optimal fractional coloring yields a merger preserving a 1/χ_f(G) fraction of the total verified local improvement. Code-repair experiments show verified merging resolves conflicts that cause naive merging to fail, fractional integration retains 922 units of verified graph-cut improvement across 90 paired runs on three public road networks, and fractional scheduling cuts measured wall time by a median of 15% across twelve paired runs of route-search agents.