TLDR: AI Workflows Need Topological Sort

Date: 2026-06-01 Source: https://arpitbhayani.me/blogs/ai-topological-sort

Overview

DAGs model AI workflows and multi-agent systems as dependency graphs where edges encode execution order constraints. Topological sort converts this graph into a valid task schedule in O(V+E) time, detects circular dependencies before execution begins, and reveals which tasks can run in parallel. For multi-agent orchestration, this means agents are dispatched only when their inputs are ready, with no hardcoded sequencing logic required.

Key Points

• Every AI workflow is a dependency problem.
• The Dependency Problem in AI Workflows: If you run step 3 before step 2 finishes, you embed dirty text.
• Modeling Workflows as DAGs: A DAG represents a workflow as a set of nodes (tasks) and directed edges (dependencies).
• Topological Sort: A topological ordering of a DAG is a sequence of all nodes such that for every edge u→v, the source node appears before the target.