Fix #110: Add LongestCommonSubsequence model and LCS to ILP reduction

[zazabap]

Summary

Adds the LongestCommonSubsequence problem model and implements the LCS-to-ILP reduction using the match-pair formulation from Blum et al. (2021).

Since the LCS model (issue #108, PR #170) has a deleted branch, this PR implements both the model and the reduction rule together.

Fixes #110

[codecov]

Codecov Report

❌ Patch coverage is 98.72774% with 5 lines in your changes missing coverage. Please review.
✅ Project coverage is 96.63%. Comparing base (cc87cf0) to head (1ee99a4).
⚠️ Report is 2 commits behind head on main.

Files with missing lines	Patch %	Lines
src/rules/longestcommonsubsequence_ilp.rs	94.04%	5 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #598      +/-   ##
==========================================
+ Coverage   96.61%   96.63%   +0.02%     
==========================================
  Files         218      222       +4     
  Lines       29352    29745     +393     
==========================================
+ Hits        28357    28745     +388     
- Misses        995     1000       +5     

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[zazabap]

Implementation Summary

Changes

• New model: src/models/misc/longest_common_subsequence.rs -- LongestCommonSubsequence problem with binary selection over shortest string, OptimizationProblem with Metric = SolutionSize<i32>, Direction::Maximize
• New rule: src/rules/longestcommonsubsequence_ilp.rs -- Match-pair ILP formulation (Blum et al. 2021) with assignment and no-crossing constraints
• Unit tests: Model tests (basic, serialization, brute force, 3-string case) + Reduction tests (closed-loop, edge cases)
• Example: examples/reduction_longestcommonsubsequence_to_ilp.rs with ABAC/BACA instance
• CLI: Registered in dispatch, problem_name (alias: LCS), create (--strings flag)
• Paper: Added problem-def, reduction-rule, and bibliography entries (maier1978, blum2021)
• Module registration: misc/mod.rs, models/mod.rs, lib.rs prelude, rules/mod.rs

Deviations from Plan

• Implemented both the LCS model ([Model] LongestCommonSubsequence #108) and the LCS-to-ILP rule ([Rule] LongestCommonSubsequence to ILP #110) in one PR since the LCS model PR Superseded: Add LongestCommonSubsequence model #170 had its branch deleted

Open Questions

• The reduction handles the 2-string case only (as specified in the issue). For k>2 strings, the brute-force solver works but the ILP reduction only uses the first two strings

[Copilot]

Pull request overview

This PR adds the LongestCommonSubsequence (LCS) problem model and implements a reduction from LCS to ILP using the match-pair formulation from Blum et al. (2021). It covers both the model (originally PR #170 whose branch was deleted) and the reduction rule (issue #110) in a single PR.

Changes:

• New LongestCommonSubsequence model with binary config over shortest string, subsequence feasibility checking, and brute-force solvability.
• New LCS-to-ILP reduction using match-pair binary variables with one-to-one matching and order-preservation (no-crossing) constraints, scoped to 2-string instances.
• Full integration: CLI dispatch/create/alias, module registration, prelude export, documentation in reductions.typ, bibliography entries, example, and comprehensive tests.

Reviewed changes

Copilot reviewed 16 out of 16 changed files in this pull request and generated 3 comments.

Show a summary per file

File	Description
src/models/misc/longest_common_subsequence.rs	New LCS model: struct, new(), evaluate(), dims(), problem registration
src/rules/longestcommonsubsequence_ilp.rs	LCS→ILP reduction: match-pair formulation, constraints, solution extraction
src/rules/mod.rs	Register the new reduction module
src/models/misc/mod.rs	Register the new model module
src/models/mod.rs	Re-export LongestCommonSubsequence
src/lib.rs	Add LongestCommonSubsequence to prelude
problemreductions-cli/src/dispatch.rs	Add LCS to load_problem() and serialize_any_problem()
problemreductions-cli/src/commands/create.rs	Add CLI --strings flag handling for LCS creation
problemreductions-cli/src/cli.rs	Add --strings CLI argument and help text
problemreductions-cli/src/problem_name.rs	Add "LCS" alias
src/unit_tests/models/misc/longest_common_subsequence.rs	14 unit tests for the model
src/unit_tests/rules/longestcommonsubsequence_ilp.rs	7 unit tests for the reduction
examples/reduction_longestcommonsubsequence_to_ilp.rs	Example with JSON export
tests/suites/examples.rs	Register the example test
docs/paper/reductions.typ	Problem definition and reduction rule documentation
docs/paper/references.bib	Add Maier 1978 and Blum 2021 references

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[Copilot]

The reduction asserts strings.len() >= 2 but only uses strings[0] and strings[1], silently ignoring any additional strings. For 3+ strings, the ILP solution would be incorrect because constraints from the extra strings are not encoded. Since this reduction is scoped to 2 strings only (as stated in the issue), this should assert strings.len() == 2 to prevent silently producing wrong results.

Suggested change

	strings.len() >= 2,
	"LCS to ILP reduction requires at least 2 strings"
	strings.len() == 2,
	"LCS to ILP reduction is defined for exactly 2 strings"

[Copilot]

The complexity string "2^total_length" is incorrect. The brute-force search space is determined by dims(), which returns vec![2; shortest_len()] — so the complexity should be 2^min_string_length (where min_string_length corresponds to the shortest string). total_length is the sum of all string lengths, which grossly overestimates the actual search space. You would need to either expose a public min_string_length() getter method for the macro to call, or rename shortest_len() to be public with an appropriate name.

Suggested change

	LongestCommonSubsequence => "2^total_length",
	LongestCommonSubsequence => "2^min_string_length",

[Copilot]

The longestcommonsubsequence_ilp module is placed between ilp_bool_ilp_i32 and ilp_qubo, breaking the alphabetical ordering used by the other modules in this block. It should be placed after knapsack_ilp or before maximumclique_ilp — actually, there's no knapsack_ilp, so it should be placed after ilp_qubo (since "l" > "i") and before maximumclique_ilp (since "l" < "m") to maintain alphabetical order.

Suggested change

	mod longestcommonsubsequence_ilp;
	#[cfg(feature = "ilp-solver")]
	mod ilp_qubo;
	#[cfg(feature = "ilp-solver")]
	mod ilp_qubo;
	#[cfg(feature = "ilp-solver")]
	mod longestcommonsubsequence_ilp;
	#[cfg(feature = "ilp-solver")]

[GiggleLiu]

Review Pipeline Report

Check	Result
Copilot comments	3 already fixed (assert ==2, complexity string, module order)
Issue/human comments	4 issue quality checks reviewed, all concerns addressed in code
Merge with main	Clean merge, no conflicts
CI	green (Clippy, Test, Coverage, Codecov all pass)
Agentic test (model)	passed — LCS creation, brute force, CLI all work
Agentic test (reduction)	passed — ILP reduction, closed-loop verification, example all work
Edge case from PR #170	Added empty string test (inspired by PR #170)
Board	review-agentic (needs manual move — auth scope missing)

Notes

• PR Fix #110: Add LongestCommonSubsequence model and LCS to ILP reduction #598 supersedes PR Superseded: Add LongestCommonSubsequence model #170 (model-only) — Superseded: Add LongestCommonSubsequence model #170 can be closed after this merges
• PR also fixes [Model] LongestCommonSubsequence #108 (LCS model) in addition to [Rule] LongestCommonSubsequence to ILP #110 (LCS-to-ILP rule)
• Minor doc improvements suggested (stale CLI docs, getting-started example) — non-blocking

🤖 Generated by review-pipeline