Fractional coloring bounds safe merges of parallel agent edits
Original title: Parallel AI Agent Collaboration as Graph-Structured Distributed Block Optimization
Verified merging keeps a 1 over fractional-chromatic-number share of local gains and cuts route wall time 15%.
The paper models parallel agent edits as discrete block optimization on a known dependency graph, where independent sets certify edits whose verified gains add exactly. An optimal fractional coloring is proved to preserve a 1/χ_f(G) share of total verified local improvement, tight among subset mergers. Code-repair tests show verified merging resolves conflicts that make naive merging fail. On three public road networks, fractional integration retained 922 units of graph-cut improvement across 90 paired runs, and route scheduling cut median wall time by 15%.
- Repeated collaboration converges geometrically under stated local-improvement conditions.
- A linear program assigns agents and exposes a time-cost trade-off.
- Conflict-free tasks finish faster in the model at higher token-equivalent cost.
- Route-cost changes varied across twelve paired runs.
From the original article
1 min read at arxiv.orgParallel AI agents can produce useful local edits yet degrade a shared solution when their edits are combined. We model this coordination problem as discrete block optimization with an exactly evaluable objective and a known dependency graph. Independent sets certify compatible edits whose verified gains, measured against the same current solution, add exactly.
By Hanmin Li · arxiv.org
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