[lgamorim]

Summary

Minor release 1.1.0: four additive algorithm milestones completing the shortest-path, flow, and connectivity suites. No breaking changes — the public API grows by 23 analyzer-tracked entries, promoted to PublicAPI.Shipped.txt at the cut.

• M46 — Biconnected and 2-edge-connected components. BiconnectedComponents (maximal edge sets sharing a simple cycle; bridges surface as single-edge components) and TwoEdgeConnectedComponents (vertex partition after removing all bridges), riding the existing iterative low-link DFS so all four connectivity views agree by construction. Closes M46: Add biconnected and 2-edge-connected components #11
• M47 — Minimum-cost maximum flow. MinCostMaximumFlow (successive shortest augmenting paths with vertex potentials) plus the MinimumCostMaximumFlow entry point; separate capacity/cost selectors, negative costs supported until a negative-cost cycle is reachable, TotalCost on the result. Closes M47: Add minimum-cost maximum flow #12
• M48 — Johnson's all-pairs shortest paths. JohnsonAllShortestPaths, the sparse alternative to Floyd-Warshall: one Bellman-Ford pass from an implicit virtual source (no graph mutation) sets potentials, then Dijkstra per source; same result type and negative-weight semantics, plus a ParallelOptions overload. Closes M48: Add Johnson's all-pairs shortest paths #13
• M49 — Lazy k-shortest-path enumeration. EnumerateShortestPaths (Yen's algorithm): a lazy sequence of simple paths in nondecreasing weight, so .Take(k) is the classic query and enumeration cost is caller-controlled. Closes M49: Add lazy k-shortest-path enumeration (Yen) #14

Release cut: version 1.1.0, [1.1.0] CHANGELOG section, both READMEs updated (feature rows, usage snippets, "1.1 is stable", test count).

Rebased onto master at 1.0.1, so the branch carries the 1.0.1 correctness fixes and packaging.

Verification

• dotnet test — 905 tests passing on both net8.0 and net10.0, zero warnings under TreatWarningsAsErrors
• dotnet pack — Graph1x.1.1.0.nupkg + .snupkg produced cleanly
• PublicAPI.Unshipped.txt empty after promotion

🤖 Generated with Claude Code

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.

📢 Thoughts on this report? Let us know!

[lgamorim]

Review: 1.1.0 cut

Ten findings, one of which should block the merge. Everything else is cleanup or coverage and can land as follow-ups if you prefer.

Blocking

Johnson path reconstruction can loop forever — JohnsonAllShortestPaths.cs#L216

Each row stores the first hop of its own Dijkstra tree, but AllPairsShortestPaths.Between reconstructs by hopping across rows (current = _next[current, to]). Rows break ties independently, so on a zero-weight cycle row a can point to b while row b points to a, and Between never terminates.

Reproduced with:

a->b 0, b->a 0, a->p 1, a->f 1, b->q 1, b->f 1, p->t 1, q->t 1   // inserted in this order
new JohnsonAllShortestPaths<...>(e => e.Weight).Compute(graph).Between("a", "t");  // hangs

Floyd-Warshall on the same graph returns distance 2. JohnsonTests only compares distances against Floyd-Warshall, never paths, so the suite is green. Fix options: make reconstruction row-local (per-row parent matrix, walk _next[from, …] only), or derive a globally consistent next matrix.

Correctness, lower likelihood

• Parent-edge skip matches by vertex, not tree-edge identity — GraphConnectivityExtensions.cs#L379. Correct for UndirectedMultigraph because both incidence lists share insertion order, but IReadOnlyGraph is public and promises no cross-endpoint ordering. A custom graph backed by per-vertex HashSet<TEdge> would list the tree edge twice and drop its parallel twin, with bridges and articulation points still correct. Skipping on Equals(edge, frame.TreeEdge) once removes the assumption. The existing parallel-edge test uses value-equal edges and asserts counts only, so it would not catch this.
• MinArcWeight returns Zero when no arc is found — GraphKShortestPathsExtensions.cs#L199. found is set but never checked. The enumerator is lazy and re-reads the live graph each MoveNext, and the library documents that mutations show through deferred enumeration, so a RemoveEdge between yields silently under-counts the root weight and later distances come out too small and non-monotone. Throwing on !found matches how CheckedWeight fails.

Cleanup

• Min-cost flow re-implements ResidualNetwork.Augment and the edge-flow loop — MinCostMaximumFlow.cs#L147. ArcCount/Tail/Flow/Origin were exported only to make the copies possible, so the "forward arcs are even" invariant now lives in two files. total += network.Augment(parentArc, sourceIndex, sinkIndex) plus an internal edge-flow enumerator next to BuildResult removes both.
• Cost list kept aligned outside AddArcPair, _cost! unjustified — ResidualNetwork.cs#L93. Any future continue between AddArcPair and the cost append shifts every later cost by one pair with no exception. Pass the cost into AddArcPair (Zero when no selector) and either drop the ! or document the invariant at the suppression site, per coding-standards.md.
• SpurDijkstra copies DijkstraShortestPath.Relax and BuildPath — GraphKShortestPathsExtensions.cs#L207. Differs only by two ban sets and a different negative-weight message. A vertex-filter parameter on the shared core plus GraphTraversalCore.BuildPath would remove the copy.
• TwoEdgeConnectedComponents clones the ConnectedComponents BFS — GraphConnectivityExtensions.cs#L262. Same flood-fill 40 lines apart with one extra skip; a private helper taking an optional edge predicate keeps one implementation.
• Bellman-Ford potentials run even when all costs are non-negative — MinCostMaximumFlow.cs#L187. With all costs ≥ 0 the zero vector is already feasible and hasPotential = all true is behaviorally identical. On a long-diameter network with unfavorable insertion order this is Θ(V·E) before the first augmentation. One O(E) sign scan skips it for the common case.

Coverage and docs

• New token overloads missing from CancellableOperations — CancellationTests.cs#L32. The new tests only pass a pre-cancelled token, which the entry-point check satisfies alone, so the per-source and per-augmentation checks are undefended. Register JohnsonAllShortestPaths.Compute, MinCostMaximumFlow.FindMinimumCostMaximumFlow, and the facade.
• AllPairsShortestPaths doc still says "Floyd-Warshall computation" — FloydWarshallAllShortestPaths.cs#L143. Johnson now returns the same type, and it still lives in the Floyd-Warshall file.

Checked and fine

Unsigned TWeight costs (every compared quantity is provably non-negative), no CancellationToken on EnumerateShortestPaths (matches the documented lazy-enumerator precedent in GraphCliqueExtensions), ResidualNetwork changes are additive for Edmonds-Karp and Dinic, PublicAPI entries match the actual signatures, and the biconnected edge-stack discipline holds on the built-in graph types.

[lgamorim]

Review response: all ten findings addressed

Thanks for the thorough pass. Every finding checked out against the code, and the blocking one reproduced exactly as described: your eight-edge graph ran Between("a", "t") until the path list exhausted memory (about 30 s) while Floyd-Warshall answered immediately. Each item landed as its own commit so they can be read, or reverted, independently.

Blocking

• Johnson path reconstruction can loop forever — fixed in f692e5e. Took the row-local option: AllPairsShortestPaths now holds a predecessor matrix, Johnson stores its Dijkstra parents directly, and Floyd-Warshall uses the textbook pred[i, j] = pred[k, j] update. Between walks a single row, which is a tree by construction, so independent tie-breaking between rows can no longer form a cycle. Your reproduction is now a test, the Floyd-Warshall comparisons validate every reconstructed path against the graph (edges exist, cheapest-arc sum equals Distance), and a new test runs random graphs dense in zero-weight cycles through both algorithms.

Correctness, lower likelihood

• Parent-edge skip matches by vertex, not tree-edge identity — a5f6b90. Skips on EqualityComparer<TEdge>.Default.Equals(edge, frame.TreeEdge) once; Parent is gone from the frame. Covered by a read-only view that reverses one vertex's incidence order over reference-identity edges, which failed before the change.
• MinArcWeight returns Zero when no arc is found — aba101b. Throws InvalidOperationException on !found, matching how the graphs report mutation during enumeration; tested by removing an edge of the yielded path between two MoveNext calls.

Cleanup

• Min-cost flow re-implements Augment and the edge-flow loop — 67298e8. total += network.Augment(...), plus internal EdgeFlows() and TotalCost() next to BuildResult. Bellman-Ford now walks IncidentArcs(tail) instead of raw arc ids, so ArcCount/Tail/Flow/Origin are removed and the even-id layout is private to ResidualNetwork again.
• Cost list kept aligned outside AddArcPair, _cost! unjustified — 396475e. Cost is passed into AddArcPair (Zero without a selector) and the remaining suppression on Cost(arc) carries a justification comment.
• SpurDijkstra copies Relax and BuildPath — 3eb1f59. New internal DijkstraCore.Relax with an optional (current, neighbor) skip filter and a caller-supplied requirement string; the public class passes no filter, the spur search expresses both ban sets through it and rebuilds with GraphTraversalCore.BuildPath.
• TwoEdgeConnectedComponents clones the BFS — a009c97. One private flood fill with an optional blocking predicate serves both methods.
• Bellman-Ford runs even when all costs are non-negative — b63bd60. ResidualNetwork.HasNegativeCost() sign scan; the zero vector is used when it is clean. Flow value and total cost are unchanged; only the tie-break between equal-cost augmenting paths can differ, and the suites assert optimality rather than a specific tie.

Coverage and docs

• Token overloads missing from CancellableOperations — b9b7670. Registered Johnson, JohnsonParallel, MinCostFlow and MinCostFlowFacade, and added mid-computation tests that cancel from inside the weight/capacity selector (which runs during setup) so the per-source and per-augmentation checks are the ones that throw.
• Doc still says "Floyd-Warshall computation" — wording fixed with the blocking commit; a894d51 moves AllPairsShortestPaths into its own file as a pure move.

Verification

dotnet test Graph1x.sln: 921 passing on net8.0 and net10.0 (up from 905), zero warnings under TreatWarningsAsErrors; dotnet format --verify-no-changes clean; no public API changes, so PublicAPI.*.txt is untouched.

[lgamorim]

Follow-up: fixes verified

All ten fixes check out against their commits and tests. Suite at a894d51: 921 passing on net8.0 and net10.0, zero warnings, PublicAPI.*.txt untouched. I also stress-ran both all-pairs reconstructions over 150 random graphs (a third with every weight zero): every path exists, is simple, and sums to its reported distance, for Floyd-Warshall and Johnson alike. Nothing blocking remains. Three minor points, none of which need to hold the merge:

1. The min-cost flow cancellation test guards a different check than its comment says. Cancelling from the capacity selector trips the ThrowIfCancellationRequested() that follows InitialPotentials, not the one inside the augmentation loop, so deleting the in-loop check alone keeps the suite green. There is no deterministic way to cancel between augmentations from outside, which is fine; the comment on MidComputation_MinCostFlowObservesCancellationBetweenAugmentations and the commit message should just describe what the test actually exercises.

2. Floyd-Warshall may now return a different path among equal-cost ties than 1.0.1 did. Switching from the next-hop matrix to the predecessor update is within contract (any shortest path is valid), but it is a user-visible change to a shipped API and the 1.1.0 section only has ### Added. A one-line ### Changed entry would match how 1.0.1 called out its behavior changes.

3. codecov/patch is the only red check. The report attributes the gap to GraphKShortestPathsExtensions.cs. Whether to add coverage or accept it is your call, but the PR stays red until one or the other.