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Feedback Arc Set ​

The Feedback Arc Set (FAS) is the set of edges to remove to make a cycle disappear. For a clump of mutually-importing modules, knowing the SCC isn't enough — you want to know which one or two imports are actually closing the loop.

The problem ​

Tarjan's SCC tells you "these 50 modules are in a cycle." That's true and unhelpful. You can't fix 50 modules at once. You want: "these 2 imports, if you remove or invert them, break every cycle in this group."

For arbitrary directed graphs, computing the minimum feedback arc set is NP-hard. We don't need optimum — we need a small, sensible set, fast.

The heuristic ​

For each SCC of size ≥ 2:

  1. Score every internal edge by a weighted combination of:

    • source module's fan-out (more imports out → more entangled),
    • source module's coupling score (composite of fan-in × fan-out),
    • whether the edge is dynamic (() => import(...)) — slightly preferred to break, since they're often already lazy.

    Coupling dominates. The intuition: removing an edge from a heavily-coupled module is more likely to expose a real architectural mistake (and pays better when fixed).

  2. Greedily pick edges — highest score first — until no cycles remain inside the SCC. We re-run SCC detection after each removal to know when to stop. For typical SCCs (≤ 20 modules) this terminates in well under a millisecond.

  3. Bound the search. For very large SCCs, we cap the candidate set so the heuristic stays fast. The desktop app shows a "search hit the limit — count is an estimate" hint when this happens; the count of cycles broken is then a lower bound.

What you see in the UI ​

Every cycle gets a "Imports that close the cycle" section listing 1–2 specific edges. Clicking one jumps to the import line in your editor. The recommendation panel shows:

Removes 7 of 12 cycles in this group.

This is the per-edge counterfactual: "if you delete (or invert) this single import, here's how many cycles in this group disappear." For small groups the count is exact; for large groups it's a lower bound (search depth was capped).

Why not just say "delete edge X"? ​

Sometimes the right fix isn't deletion. It's:

  • Invert the import direction — pull the dependency the other way.
  • Move the type to a shared module — if both sides import a common type from each other, the type is the real shared dependency.
  • Convert to import type — if all uses are types, this is the cheapest fix possible and Archora flags it as a separate type-only candidate.

Archora only points at the edge. Choosing how to remove it is your call.

See also ​