Fix accidentally quadratic add_slacks_to_basis in crossover

[nguidotti]

When the problem is very large and the basis is extremely rank deficient, the crossover needs to add millions of slack variables to compensate.

This process can take a long time and may violate the time limit set by the user.

This PR fixes the accidentally quadratic add_slacks_to_basis in crossover that was causing the large amount of time.

[coderabbitai]

📝 Walkthrough

Walkthrough

add_slacks_to_basis now precomputes a row->singleton-slack-column map and uses it to mark BASIC slack variables for dependent rows. After calling it when rank < m, crossover verifies num_basic + rank == m and returns NUMERICAL_ISSUES if the basis is not full-rank.

Changes

Slack insertion and basis validation

Layer / File(s)	Summary
Precompute singleton slack map and assign slacks cpp/src/dual_simplex/crossover.cpp	add_slacks_to_basis builds a slack_map from singleton slack columns (nz==1) to their row and marks those slack columns BASIC for each dependent_row instead of scanning all candidate columns per row.
Validate full-rank initial basis in crossover cpp/src/dual_simplex/crossover.cpp	After adding slacks when rank < m, crossover checks num_basic + rank == m; if false it logs an error and returns crossover_status_t::NUMERICAL_ISSUES.

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🎯 3 (Moderate) | ⏱️ ~20 minutes

🚥 Pre-merge checks | ✅ 4 | ❌ 1

❌ Failed checks (1 warning)

Check name	Status	Explanation	Resolution
Docstring Coverage	⚠️ Warning	Docstring coverage is 0.00% which is insufficient. The required threshold is 80.00%.	Write docstrings for the functions missing them to satisfy the coverage threshold.

✅ Passed checks (4 passed)

Check name	Status	Explanation
Linked Issues check	✅ Passed	Check skipped because no linked issues were found for this pull request.
Out of Scope Changes check	✅ Passed	Check skipped because no linked issues were found for this pull request.
Title check	✅ Passed	The title accurately describes the main change: optimizing the accidentally quadratic add_slacks_to_basis function to be linear, which directly addresses the performance issue documented in the PR objectives.
Description check	✅ Passed	The PR description accurately describes the changeset - it identifies a performance issue with quadratic complexity in add_slacks_to_basis and explains the fix to optimize the algorithm.

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✨ Finishing Touches

🧪 Generate unit tests (beta)

• Create PR with unit tests

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[mlubin]

How much time can this take for millions of variables? It seems like a simple loop to me unless I'm misreading the code.

[nguidotti]

How much time can this take for millions of variables? It seems like a simple loop to me unless I'm misreading the code.

It is a $n^2$ loop at the worse case, right? For a time limit of 300s, this loop starts at 255s and do not finish for that time limit. The problem has 7432334 constraints, 5907688 variables

[chris-maes]

@mlubin @nguidotti It's O ( n * | dependent rows | ). Let me fix it so that it is O(m + | dependent rows |) = O(m).

[copy-pr-bot]

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[coderabbitai]

Actionable comments posted: 1

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ℹ️ Review info

⚙️ Run configuration

Configuration used: Path: .coderabbit.yaml

Review profile: CHILL

Plan: Enterprise

Run ID: 2672aefd-da6c-4e35-a248-05094ea273b0

📥 Commits

Reviewing files that changed from the base of the PR and between e35a029 and d59146c.

📒 Files selected for processing (1)

• cpp/src/dual_simplex/crossover.cpp

[chris-maes]

/ok to test d59146c

[chris-maes]

LGTM

[chris-maes]

/merge