Design: recategorize problem models by input structure

Current categorization mixes input structure (graph, set) with problem
type (optimization, satisfaction). Reorganize into orthogonal categories
based solely on input structure: graph/, formula/, set/, algebraic/, misc/.

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

Author: GiggleLiu

.claude/CLAUDE.md

@@ -49,7 +49,12 @@ make release V=x.y.z  # Tag and push a new release (CI publishes to crates.io)
 ## Architecture
 
 ### Core Modules
-- `src/models/` - Problem implementations (SAT, Graph, Set, Optimization)
+- `src/models/` - Problem implementations organized by input structure:
+  - `graph/` - Problems on graphs (MIS, MaxClique, MaxCut, MinVC, MinDS, MaxMatching, MaximalIS, KColoring, TSP, SpinGlass, BicliqueCover)
+  - `formula/` - Logical formulas and circuits (SAT, k-SAT, CircuitSAT)
+  - `set/` - Set systems (MinSetCovering, MaxSetPacking)
+  - `algebraic/` - Matrices, linear systems, lattices (QUBO, ILP, CVP, BMF)
+  - `misc/` - Unique input structures (BinPacking, PaintShop, Factoring)
 - `src/rules/` - Reduction rules + inventory registration
 - `src/solvers/` - BruteForce solver, ILP solver (feature-gated)
 - `src/traits.rs` - `Problem`, `OptimizationProblem`, `SatisfactionProblem` traits
@@ -140,7 +145,7 @@ Reduction graph nodes use variant key-value pairs from `Problem::variant()`:
 
 ### File Naming
 - Reduction files: `src/rules/<source>_<target>.rs` (e.g., `maximumindependentset_qubo.rs`)
-- Model files: `src/models/<category>/<name>.rs` (e.g., `maximum_independent_set.rs`)
+- Model files: `src/models/<category>/<name>.rs` — category is by input structure: `graph/` (graph input), `formula/` (boolean formula/circuit), `set/` (universe + subsets), `algebraic/` (matrix/linear system/lattice), `misc/` (other)
 - Example files: `examples/reduction_<source>_to_<target>.rs` (must have `pub fn run()` + `fn main() { run() }`)
 - Test naming: `test_<source>_to_<target>_closed_loop`
 

docs/plans/2026-03-01-problem-categorization-design.md

@@ -0,0 +1,84 @@
+# Problem Categorization Redesign
+
+## Problem
+
+The current categorization mixes two axes:
+- **Input structure** (graph, set system, formula)
+- **Problem type** (optimization vs satisfaction)
+
+This creates ambiguity: MIS is both a graph problem and an optimization problem. QUBO is on a matrix but lives in `optimization/`. CircuitSAT is a satisfiability problem but lives in `specialized/`. The `specialized/` folder is a catch-all with no unifying principle.
+
+## Design
+
+**Single axis: primary input structure** — "what data type does the problem operate on?"
+
+The optimization/satisfaction distinction is already captured by the trait hierarchy (`OptimizationProblem` vs `SatisfactionProblem`), so folders should not duplicate it.
+
+### New folder structure
+
+```
+src/models/
+├── graph/          # Input: a graph (optionally weighted)
+│   ├── maximum_independent_set.rs
+│   ├── maximum_clique.rs
+│   ├── max_cut.rs
+│   ├── maximum_matching.rs
+│   ├── minimum_vertex_cover.rs
+│   ├── minimum_dominating_set.rs
+│   ├── maximal_is.rs
+│   ├── kcoloring.rs
+│   ├── traveling_salesman.rs
+│   ├── spin_glass.rs          ← from optimization/
+│   └── biclique_cover.rs      ← from specialized/
+│
+├── formula/        # Input: a logical formula or circuit
+│   ├── sat.rs
+│   ├── ksat.rs
+│   └── circuit.rs             ← from specialized/
+│
+├── set/            # Input: universe + collection of subsets
+│   ├── minimum_set_covering.rs
+│   └── maximum_set_packing.rs
+│
+├── algebraic/      # Input: matrix, linear system, or lattice
+│   ├── qubo.rs                ← from optimization/
+│   ├── ilp.rs                 ← from optimization/
+│   ├── closest_vector_problem.rs  ← from optimization/
+│   └── bmf.rs                 ← from specialized/
+│
+└── misc/           # Problems with unique input structures
+    ├── bin_packing.rs         ← from optimization/
+    ├── paintshop.rs           ← from specialized/
+    └── factoring.rs           ← from specialized/
+```
+
+### Decision rule for new problems
+
+> "What is the primary data structure in the struct definition?"
+> - Graph → `graph/`
+> - Boolean formula or circuit → `formula/`
+> - Universe + subsets → `set/`
+> - Matrix, linear system, or lattice → `algebraic/`
+> - None of the above → `misc/`
+
+### What moves
+
+| Problem | From | To | Reason |
+|---|---|---|---|
+| SpinGlass | optimization/ | graph/ | Parameterized by G, operates on graph edges |
+| BicliqueCover | specialized/ | graph/ | Input is a BipartiteGraph |
+| CircuitSAT | specialized/ | formula/ | Input is a boolean circuit |
+| QUBO | optimization/ | algebraic/ | Input is a Q matrix (no graph param) |
+| ILP | optimization/ | algebraic/ | Input is constraint matrix + objective |
+| CVP | optimization/ | algebraic/ | Input is lattice basis matrix |
+| BMF | specialized/ | algebraic/ | Input is a boolean matrix |
+| BinPacking | optimization/ | misc/ | Input is items + capacity |
+| PaintShop | specialized/ | misc/ | Input is a car sequence |
+| Factoring | specialized/ | misc/ | Input is an integer |
+
+### What doesn't change
+
+- Trait hierarchy (`OptimizationProblem`, `SatisfactionProblem`)
+- All public API, type names, re-exports
+- Only `mod.rs` files, `use` paths, and `#[path]` test references change
+- The `optimization/` and `specialized/` folders are eliminated