Harden exact solve status handling and reduce DW memory

[berendmarkhorst]

Summary

• make HiGHS and Gurobi termination handling explicit across the core cut loop, SAP, prize-collecting, budget, and MWCSPB runners
• return only independently connectivity-valid incomplete incumbents, always with an unknown (inf) gap unless an independent bound provides a conservative nonzero certificate
• discard stale pre-cut values when the global deadline expires before the required re-solve; public APIs now raise when no valid incomplete incumbent exists
• preserve historical tuple shapes by making internal status fields opt-in via return_status=True
• reject negative edge/arc costs at edge-cost Steiner entry points while retaining negative MWCS node weights and topology-only MWCSPB edge attributes
• clamp the MWCSP-to-PCSTP shift at zero so all-positive node-weight instances no longer create invalid negative transformed edge costs
• reduce Dreyfus-Wagner forward-pass memory to label arrays only and recompute split/predecessor data along the final reconstruction path

Status and validation coverage

Regression tests cover tiny positive time limits, no incumbent, proven infeasibility, valid-but-unproven incumbents, expiry immediately after violated cuts, preprocessing, SAP/transformed and specialized paths, and both HiGHS and licensed Gurobi backends. They also cover the disconnected negative-cycle counterexample, custom arc-weight attributes, transform entry points, MWCS negative node weights, and Dreyfus-Wagner tied paths, zero weights, disconnected graphs, and ILP-oracle comparisons.

Dreyfus-Wagner benchmark

Compared origin/main at 90a587d with this implementation using fresh subprocesses, fixed seed 20260904, three repetitions per case, and identical Python 3.13.4 / NetworkX 3.5 / SciPy 1.17.0 environments. f is the target edge factor (m = f*n). Every objective matched.

k	n	f	main ms	candidate ms	cand/main	main RSS MiB	candidate RSS MiB	RSS delta MiB
6	300	3	3.026	3.782	1.250	71.1	71.2	+0.0
6	300	8	3.681	4.703	1.278	72.0	72.1	+0.0
6	1200	3	10.060	12.475	1.240	73.7	73.3	-0.4
6	1200	8	13.820	17.335	1.254	76.6	76.4	-0.2
7	300	3	5.720	6.249	1.092	71.3	71.3	-0.0
7	300	8	6.411	7.151	1.115	72.2	71.9	-0.3
7	1200	3	18.875	20.336	1.077	74.6	73.8	-0.8
7	1200	8	23.344	26.450	1.133	77.7	76.7	-1.0
8	300	3	11.063	11.056	0.999	71.8	71.2	-0.6
8	300	8	11.928	12.363	1.036	72.7	72.4	-0.4
8	1200	3	38.098	39.278	1.031	76.3	74.3	-2.0
8	1200	8	42.566	45.193	1.062	79.4	77.6	-1.8
9	300	3	22.404	21.937	0.979	72.9	71.9	-1.0
9	300	8	23.738	23.526	0.991	73.7	72.6	-1.1
9	1200	3	78.033	76.759	0.984	79.8	75.7	-4.1
9	1200	8	83.400	82.588	0.990	83.0	78.7	-4.2
10	300	3	49.507	45.519	0.919	74.7	72.5	-2.3
10	300	8	48.145	45.599	0.947	75.6	73.4	-2.2
10	1200	3	166.402	151.494	0.910	86.4	78.7	-7.8
10	1200	8	169.626	164.295	0.969	89.6	81.7	-7.9

The median runtime ratio across the matrix was 1.034, so this PR makes no general runtime-improvement claim. Median process RSS changed by -1.0 MiB across all cases; the largest measured reduction was 7.9 MiB at k=10, n=1200.

Nested-cut profiling

On a fixed n=600, m=3600, 60-terminal separation workload (nested=1, one separation thread, 20 profiled calls), CSR construction accounted for 0.163 s of 2.850 s total (5.7%), versus 1.617 s cumulative max-flow time. A prototype per-thread CSR cache reduced construction calls from 1200 to 20, but nine unprofiled repetitions were indistinguishable: 0.085434 s cached versus 0.085517 s on main. The prototype was reverted and this PR contains no nested-cut change.

Validation

• python3 -m pytest -q: 795 passed, 26 skipped, 20 xpassed
• GitHub Actions: Python 3.8, 3.9, 3.10, 3.11, and 3.12 jobs all pass
• new standalone files: Black clean; flake8 clean with E501 ignored to match the configured Black line length
• full flake8 baseline comparison (E501 ignored): 152 findings here versus 156 on main
• full mypy baseline comparison (--ignore-missing-imports): 69 existing findings here versus 71 on main; isolated new files pass with --follow-imports=skip
• git diff --check and compileall: clean
• warning-strict Sphinx was attempted, but the local iCloud-backed virtual environment blocked at zero CPU while importing a SciPy binary extension; it was interrupted before document parsing and emitted no documentation warning

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Codecov Report

❌ Patch coverage is 76.10922% with 70 lines in your changes missing coverage. Please review.

Files with missing lines	Patch %	Lines
steinerpy/mathematical_model.py	68.39%	61 Missing ⚠️
steinerpy/objects.py	85.00%	9 Missing ⚠️

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