Topological Ordering and Dependency Resolution¶

In directed acyclic graphs, nodes can be linearly ordered such that all edges point forward; this ordering enables sequential processing respecting all dependencies.

Tension Addressed¶

Online vs. Offline (requires complete dependency graph; incremental updates are complex)

Recognizable As¶

Build systems, package managers, spreadsheet recalculation, course prerequisites; detected via DFS finishing times or Kahn's algorithm (in-degree tracking).

Canonical Sources¶

Kahn, "Topological Sorting of Large Networks," 1962; Tarjan, "Depth-First Search and Linear Graph Algorithms," 1972

Transfers To¶

Compiler instruction scheduling, task scheduling, data pipeline orchestration, neural network layer ordering

The existence of topological order is equivalent to the absence of cycles. Cycle detection is thus a prerequisite check; detected cycles indicate circular dependencies that must be resolved before ordering.