feat: variant-aware reduction paths with resolve_path

benches/solver_benchmarks.rs

@@ -8,6 +8,7 @@ use problemreductions::models::set::*;
 use problemreductions::models::specialized::*;
 use problemreductions::prelude::*;
 use problemreductions::topology::SimpleGraph;
+use problemreductions::variant::K3;
 use std::hint::black_box;
 
 /// Benchmark MaximumIndependentSet on graphs of varying sizes.
@@ -138,7 +139,7 @@ fn bench_coloring(c: &mut Criterion) {
 
     for n in [3, 4, 5, 6].iter() {
         let edges: Vec<(usize, usize)> = (0..*n - 1).map(|i| (i, i + 1)).collect();
-        let problem = KColoring::<3, SimpleGraph>::new(*n, edges);
+        let problem = KColoring::<K3, SimpleGraph>::new(*n, edges);
         let solver = BruteForce::new();
 
         group.bench_with_input(BenchmarkId::new("path_3colors", n), n, |b, _| {

book.toml

@@ -9,8 +9,8 @@ src = "docs/src"
 default-theme = "navy"
 git-repository-url = "https://github.com/CodingThrust/problem-reductions"
 edit-url-template = "https://github.com/CodingThrust/problem-reductions/edit/main/{path}"
-additional-css = ["docs/src/static/theme-images.css"]
-additional-js = []
+additional-css = ["docs/src/static/theme-images.css", "docs/src/static/reduction-graph.css"]
+additional-js = ["docs/src/static/cytoscape.min.js", "docs/src/static/reduction-graph.js"]
 no-section-label = false
 
 [output.html.fold]

docs/paper/lib.typ

@@ -93,27 +93,25 @@
 
 // King's subgraph from JSON with weight-based coloring
 #let draw-grid-graph(data, cell-size: 0.2) = canvas(length: 1cm, {
-  let grid-data = data.grid_graph
-  let positions = grid-data.nodes.map(n => (n.col * cell-size, -n.row * cell-size))
-  let fills = grid-data.nodes.map(n => weight-color(n.weight))
-  let edges = grid-data.edges.map(e => (e.at(0), e.at(1)))
+  let positions = data.nodes.map(n => (n.col * cell-size, -n.row * cell-size))
+  let fills = data.nodes.map(n => weight-color(n.weight))
+  let edges = data.edges.map(e => (e.at(0), e.at(1)))
   for (u, v) in edges { g-edge(positions.at(u), positions.at(v), stroke: 0.4pt + gray) }
   for (k, pos) in positions.enumerate() {
     g-node(pos, radius: 0.04, stroke: none, fill: fills.at(k))
   }
 })
 
 // Triangular lattice from JSON with weight-based coloring
-// Matches Rust GridGraph::physical_position_static for Triangular (offset_even_cols=true)
+// Physical positions use triangular lattice transform (offset_even_cols=true)
 #let draw-triangular-graph(data, cell-size: 0.2) = canvas(length: 1cm, {
-  let grid-data = data.grid_graph
   let sqrt3_2 = calc.sqrt(3) / 2
-  let positions = grid-data.nodes.map(n => {
+  let positions = data.nodes.map(n => {
     let offset = if calc.rem(n.col, 2) == 0 { 0.5 } else { 0.0 }
     ((n.row + offset) * cell-size, -n.col * sqrt3_2 * cell-size)
   })
-  let fills = grid-data.nodes.map(n => weight-color(n.weight))
-  let edges = grid-data.edges.map(e => (e.at(0), e.at(1)))
+  let fills = data.nodes.map(n => weight-color(n.weight))
+  let edges = data.edges.map(e => (e.at(0), e.at(1)))
   for (u, v) in edges { g-edge(positions.at(u), positions.at(v), stroke: 0.3pt + gray) }
   for (k, pos) in positions.enumerate() {
     g-node(pos, radius: 0.025, stroke: none, fill: fills.at(k))

docs/paper/reductions.typ

@@ -43,8 +43,8 @@
   "KSatisfiability": [$k$-SAT],
   "CircuitSAT": [CircuitSAT],
   "Factoring": [Factoring],
-  "GridGraph": [GridGraph MIS],
-  "Triangular": [Triangular MIS],
+  "KingsSubgraph": [King's Subgraph MIS],
+  "TriangularSubgraph": [Triangular Subgraph MIS],
 )
 
 // Definition label: "def:<ProblemName>" — each definition block must have a matching label
@@ -828,7 +828,7 @@ The following reductions to Integer Linear Programming are straightforward formu
 
 == Unit Disk Mapping
 
-#reduction-rule("MaximumIndependentSet", "GridGraph")[
+#reduction-rule("MaximumIndependentSet", "KingsSubgraph")[
   @nguyen2023 Any MIS problem on a general graph $G$ can be reduced to MIS on a unit disk graph (King's subgraph) with at most quadratic overhead in the number of vertices.
 ][
   _Construction (Copy-Line Method)._ Given $G = (V, E)$ with $n = |V|$:
@@ -885,7 +885,7 @@ The following reductions to Integer Linear Programming are straightforward formu
   caption: [Unit disk mappings of the Petersen graph. Blue: weight 1, red: weight 2, green: weight 3.],
 ) <fig:petersen-mapping>
 
-#reduction-rule("MaximumIndependentSet", "Triangular")[
+#reduction-rule("MaximumIndependentSet", "TriangularSubgraph")[
   @nguyen2023 Any MIS problem on a general graph $G$ can be reduced to MIS on a weighted triangular lattice graph with at most quadratic overhead in the number of vertices.
 ][
   _Construction._ Same copy-line method as the KSG mapping, but uses a triangular lattice instead of a square grid. Crossing and simplifier gadgets are adapted for triangular geometry, producing a unit disk graph on a triangular grid where edges connect nodes within unit distance under the triangular metric.

docs/paper/static/petersen_source.json

@@ -1,67 +1 @@
-{
-  "name": "Petersen",
-  "num_vertices": 10,
-  "edges": [
-    [
-      0,
-      1
-    ],
-    [
-      1,
-      2
-    ],
-    [
-      2,
-      3
-    ],
-    [
-      3,
-      4
-    ],
-    [
-      4,
-      0
-    ],
-    [
-      5,
-      7
-    ],
-    [
-      7,
-      9
-    ],
-    [
-      9,
-      6
-    ],
-    [
-      6,
-      8
-    ],
-    [
-      8,
-      5
-    ],
-    [
-      0,
-      5
-    ],
-    [
-      1,
-      6
-    ],
-    [
-      2,
-      7
-    ],
-    [
-      3,
-      8
-    ],
-    [
-      4,
-      9
-    ]
-  ],
-  "mis": 4
-}
+{"name":"Petersen","num_vertices":10,"edges":[[0,1],[1,2],[2,3],[3,4],[4,0],[5,7],[7,9],[9,6],[6,8],[8,5],[0,5],[1,6],[2,7],[3,8],[4,9]],"mis":4}