feat: One weight IS↔SP variants, fix complexity metadata, enrich paper

[GiggleLiu]

Summary

• Add One weight variant for MaximumIndependentSet ↔ MaximumSetPacking reductions
• Remove dead APIs: ConfigIterator, unused testing module, LinearConstraint::new() publicity
• Fix 7 wrong declare_variants! complexity strings (poly-time problems had exponential bounds)
• Fix 4 wrong #[reduction(overhead)] formulas (universe mismatch, quadratic edges, cell counts)
• Re-export reduction_graph.json with corrected data
• Remove standalone complexity table from paper; show complexity inline via render-complexity
• Enrich all 21 problem definitions with algorithm context, limitations, and citations

Test plan

• All 1628 tests pass (cargo test)
• Clippy clean
• Paper compiles with no warnings (typst compile)
• Reduction graph JSON regenerated with correct overheads

🤖 Generated with Claude Code

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 96.88%. Comparing base (13249b3) to head (c24294a).
⚠️ Report is 1 commits behind head on main.

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #106      +/-   ##
==========================================
- Coverage   96.89%   96.88%   -0.02%     
==========================================
  Files         198      196       -2     
  Lines       26904    26747     -157     
==========================================
- Hits        26068    25913     -155     
+ Misses        836      834       -2     

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[Copilot]

Pull request overview

This PR extends the reduction/variant metadata system by adding a unit-weight (One) variant for the MaximumIndependentSet ↔ MaximumSetPacking reductions, correcting complexity/overhead metadata used to generate the reduction graph and paper, and removing unused/dead testing/config APIs.

Changes:

• Add One weight variants for MIS ↔ Set Packing reductions and variant-cast support for MaximumSetPacking.
• Fix/refresh complexity + reduction-overhead metadata and regenerate reduction_graph.json; render complexity inline in the paper.
• Remove dead APIs and test utilities (testing module, ConfigIterator) and update unit tests accordingly.

Reviewed changes

Copilot reviewed 21 out of 21 changed files in this pull request and generated 5 comments.

Show a summary per file

File	Description
src/unit_tests/testing/mod.rs	Removes tests for the deleted testing utilities module.
src/unit_tests/testing/macros.rs	Removes macro tests for deleted testing macros.
src/unit_tests/rules/maximumindependentset_maximumsetpacking.rs	Adds closed-loop tests for One-weighted MIS ↔ SP reductions.
src/unit_tests/config.rs	Removes tests tied to deleted ConfigIterator; keeps conversion + dims iterator tests.
src/testing/mod.rs	Deletes the public testing utilities module (macros + test-case structs).
src/testing/macros.rs	Deletes exported testing macros (graph_problem_tests!, complement_test!, quick_problem_test!).
src/rules/sat_ksat.rs	Updates #[reduction(overhead)] formulas for SAT → 3-SAT transformation.
src/rules/maximumsetpacking_casts.rs	Adds variant-cast reduction MaximumSetPacking<One> => MaximumSetPacking<i32>.
src/rules/maximumindependentset_maximumsetpacking.rs	Generalizes MIS ↔ SP reductions to support both i32 and One; fixes overhead field mapping.
src/rules/factoring_circuit.rs	Updates reduction overhead metadata for Factoring → CircuitSAT.
src/models/set/maximum_set_packing.rs	Declares MaximumSetPacking<One> variant complexity.
src/models/satisfiability/ksat.rs	Fixes K2 (2-SAT) declared complexity to polynomial time.
src/models/optimization/ilp.rs	Makes LinearConstraint::new crate-private.
src/models/graph/maximum_matching.rs	Fixes declared complexity to polynomial time (n^3).
src/models/graph/kcoloring.rs	Updates declared complexities for K-coloring variants.
src/lib.rs	Removes pub mod testing export.
src/config.rs	Removes ConfigIterator and tightens module docs around DimsIterator.
docs/src/reductions/reduction_graph.json	Regenerates graph JSON with updated complexities, nodes/edges, and overhead formulas.
docs/paper/references.bib	Adds citations supporting updated complexity claims.
docs/paper/reductions.typ	Renders complexity inline from graph JSON; enriches problem definitions with algorithm context.
.claude/CLAUDE.md	Documents how to verify declare_variants! complexity and #[reduction(overhead)] formulas.

Comments suppressed due to low confidence (1)

src/config.rs:6

• ConfigIterator has been removed from the public config API. Even if it was unused internally, this is a breaking change for downstream users who relied on it for uniform-dimension iteration. If intentional, consider documenting the replacement (e.g., DimsIterator::new(vec![num_flavors; num_variables])) and accounting for the API break in versioning/release notes.

//! Configuration utilities for problem solving.

/// Convert a configuration index to a configuration vector.
///
/// The index is treated as a number in base `num_flavors`.
pub fn index_to_config(index: usize, num_variables: usize, num_flavors: usize) -> Vec<usize> {

---

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[Copilot]

KColoring<K5, SimpleGraph> is declared with complexity 2^num_vertices, but the paper text in docs/paper/reductions.typ states 5-coloring has an algorithm that breaks the 2^n barrier (Zamir 2021). To keep the rendered complexity (from declare_variants!) consistent with the paper and with the “best known algorithm” convention, update this complexity string (or adjust the paper text if you intentionally want an upper bound).

Suggested change

	KColoring<K5, SimpleGraph> => "2^num_vertices",
	KColoring<K5, SimpleGraph> => "<2^num_vertices",

[Copilot]

This section claims 5-coloring runs in $O^*((2-\epsilon)^n)$, but the rendered complexity line for KColoring is sourced from reduction_graph.json / declare_variants! (currently KColoring<K5> is 2^num_vertices). Align the complexity metadata with this claim (or soften the claim) so the paper doesn’t present conflicting complexities.

Suggested change

Deciding $k$-colorability is NP-complete for $k >= 3$ @garey1979. Best known: $O(n+m)$ for $k=2$ (equivalent to bipartiteness testing by BFS); $O^*(1.3289^n)$ for $k=3$ @beigel2005; $O^*(1.7159^n)$ for $k=4$ @wu2024; $O^*((2-epsilon)^n)$ for $k=5$, the first to break the $2^n$ barrier @zamir2021; $O^*(2^n)$ in general via inclusion-exclusion over independent sets @bjorklund2009.

Deciding $k$-colorability is NP-complete for $k >= 3$ @garey1979. Best known upper bounds for deciding $k$-colorability include: $O(n+m)$ for $k=2$ (equivalent to bipartiteness testing by BFS); $O^*(1.3289^n)$ for $k=3$ @beigel2005; $O^*(1.7159^n)$ for $k=4$ @wu2024; $O^*(2^n)$ for $k >= 5$ via inclusion-exclusion over independent sets @bjorklund2009; and faster sub-$2^n$ algorithms are known for $k=5$ @zamir2021.

[Copilot]

Removing pub mod testing; is a breaking public API change (downstream users can no longer import problemreductions::testing / its macros). If this is intentional, consider documenting it in release notes and ensuring the versioning strategy accounts for the break.

[Copilot]

Changing LinearConstraint::new from pub to pub(crate) is a breaking change for external users that constructed constraints via new. If the intent is to force callers onto le/ge/eq, consider noting this in release notes and (optionally) adding a doc comment/deprecation path to guide downstream migration.

Suggested change

	pub(crate) fn new(terms: Vec<(usize, f64)>, cmp: Comparison, rhs: f64) -> Self {
	pub fn new(terms: Vec<(usize, f64)>, cmp: Comparison, rhs: f64) -> Self {

[Copilot]

The num_assignments overhead doesn’t match what reduce_to() constructs. The reduction adds 6 assignments per multiplier cell plus one additional assignment per output bit constraint (loop over m_vars), i.e. num_bits_first + num_bits_second extra assignments. Update the overhead formula accordingly and regenerate docs/src/reductions/reduction_graph.json so the exported graph matches the code.

Suggested change

	num_assignments = "6 * num_bits_first * num_bits_second",
	num_assignments = "6 * num_bits_first * num_bits_second + num_bits_first + num_bits_second",