Luigi (Python) — CWE-407 Disclosure Brief

2026-03-27 · Patch available — awaiting upstream merge

Finding

One O(n²) defect in Luigi's dependency path finder — in the recursive DFS used for task dependency visualization. Patched. Patch ready for upstream review. Luigi is Spotify's Python pipeline framework, widely used for data engineering and ETL workflows.

The Defect

luigi-0001 (PATCHED — MEDIUM): luigi/tools/deps.py:dfs_paths

# In dfs_paths() — recursive DFS for dependency path enumeration:
def dfs_paths(graph, source, goal):
    stack = [(source, [source])]
    while stack:
        (vertex, path) = stack.pop()
        for next_vertex in graph[vertex] - set(path):  # set(path) rebuilt from list each call
            if next_vertex == goal:
                yield path + [next_vertex]
            else:
                stack.append((next_vertex, path + [next_vertex]))

set(path) is rebuilt from the path list on every recursive DFS call. For a path of length D and N nodes in the graph: set construction is O(D) per call, called O(N) times = O(N × D) total set constructions. Additionally, path grows as a list by appending and is copied at each step — O(D) copy overhead per level.

The combined cost: O(N × D²) for set rebuilds and list copies at each DFS step.

Complexity Proof

For a task dependency graph with N tasks and maximum path depth D:

Per DFS step: set(path) rebuilt — O(D) construction from growing list
O(N) DFS steps: O(N × D) total set construction cost
List copy per step (path + [next_vertex]): O(D) per step, O(N × D) total

At N=500 tasks, D=50 depth: defective=500 × 50 = 25,000 set construction ops (each O(50)), fixed=500 set lookups (O(1) each). Significant reduction in deep task graphs.

The fix: pass a set directly alongside the path, maintaining it incrementally (add on push, discard on pop) rather than rebuilding from scratch on every step.

Impact

Luigi is Spotify's Python pipeline framework, widely adopted in data engineering for:

ETL (Extract, Transform, Load) pipelines
Data warehouse task orchestration
Machine learning feature engineering pipelines
Batch data processing workflows

dfs_paths() is called by luigi.tools.deps — the dependency visualization and analysis tool. It is used for:

luigi-graph command for dependency visualization
Debugging complex pipeline dependency structures
Identifying dependency bottlenecks in large pipeline graphs

Large data pipelines with hundreds of tasks and deep dependency chains — common in production data warehouses — hit worst case. Teams using Luigi for complex ETL pipelines with many interdependent tasks pay this overhead when analyzing pipeline structure.

The Fix

Maintain visited set incrementally instead of rebuilding from list:

# Before
def dfs_paths(graph, source, goal):
    stack = [(source, [source])]
    while stack:
        (vertex, path) = stack.pop()
        for next_vertex in graph[vertex] - set(path):  # O(D) set rebuild per step
            # ...

# After
# CWE-407 fix: maintain path_set incrementally for O(1) membership instead of O(D) set(path).
def dfs_paths(graph, source, goal):
    stack = [(source, [source], {source})]  # (vertex, path_list, path_set)
    while stack:
        (vertex, path, path_set) = stack.pop()
        for next_vertex in graph[vertex] - path_set:  # O(1) set difference
            new_path_set = path_set | {next_vertex}   # O(1) set union
            if next_vertex == goal:
                yield path + [next_vertex]
            else:
                stack.append((next_vertex, path + [next_vertex], new_path_set))

The path set is maintained alongside the path list — no repeated construction from scratch.

Patch

Fix available: defects/luigi/patch/luigi-0001-deps-dfs-path-set.patch

Single-function change in luigi/tools/deps.py.

Unit test: O(N×D²) → O(N×D) growth confirmed. Dependency analysis speedup measurable on pipeline graphs with D>20 depth.

What We Ask

A patch is ready for review.

Confirm receipt and assign a GitHub issue reference (spotify/luigi).
Assess severity — luigi-0001 fires in dependency path analysis for every deep pipeline dependency graph; large production data pipelines are worst case.
Coordinate a disclosure date — we are targeting 90 days from first contact.
We will credit the Luigi/Spotify team in the public disclosure. Preferred acknowledgment format welcome.

Contact: see cover email. This brief is confidential until coordinated disclosure.

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