[ENH] set_cover Python: expose the lower bound accessors directly

[jg-codes]

[ENH] set_cover Python: expose the lower bound accessors directly

Disclosure: drafted with AI assistance (Claude). See the verification section for exactly what was built and run.

What

DualAscentOptimizer computes a dual lower bound and stores it on the invariant:

// ortools/set_cover/set_cover_heuristics.cc:1314
inv()->ReportLowerBound(max_lower_bound, /*is_cost_consistent=*/false);

SetCoverInvariant exposes it in C++ at set_cover_invariant.h:146 (LowerBound()) and :131 (CostOrLowerBound()). Neither is bound in ortools/set_cover/python/set_cover.cc.

The value is reachable from Python today, just indirectly: ExportSolutionAsProto() writes it into SetCoverSolutionResponse.cost_lower_bound at set_cover_invariant.cc:536, and that binding exists.

bound = inv.export_solution_as_proto().cost_lower_bound

That serializes the whole solution (selected subsets, cost, all of it) to read one scalar. This patch binds the accessor directly, next to the existing cost binding:

gap = (inv.cost() - inv.lower_bound()) / inv.cost()

For applied work that gap is the difference between handing a planner a depot network and handing them a network with a statement about how much room is left. The number already exists; this is about it sitting next to cost(), where a caller looking for it would expect to find it.

Changes

• ortools/set_cover/python/set_cover.cc: three .def() lines on SetCoverInvariant, next to the existing cost binding: lower_bound(), cost_or_lower_bound(), is_cost_consistent().
• ortools/set_cover/python/set_cover_test.py: two tests.

is_cost_consistent() is included deliberately. ReportLowerBound() is called with is_cost_consistent=false, and CostOrLowerBound() switches on that flag, so without it a caller cannot tell which of the two numbers they just received.

No new dependency, no build change.

Verification

Built and tested on Linux (Bazel 8.7.0, x86_64) against main at d9c0910:

bazel test //ortools/set_cover/python:set_cover_test   PASSED

clang-format clean against the repo .clang-format; the Python is black clean at the file's existing line width.

I also exercised the end-to-end path this patch is meant to unblock, using a temporary local benchmark script against the same build: DualAscentOptimizer.optimize() followed by inv.lower_bound() returns a non-trivial bound on real OR-Library SCP instances (see #5122 for the numbers). That path could not be checked before, since DualAscentOptimizer is not in the released PyPI wheel this PR was originally drafted against.

Checklist

• Read CONTRIBUTING.md and the PR template, targeting main
• CLA signed
• Minimal diff: three bindings and their tests
• No unrelated formatting or refactoring
• AI-assisted: disclosed above

[jg-codes]

For context: this depends on nothing else open right now, but is part of the same set_cover wrapper audit as #5121, #5122, and #5278.