Fix #534: Add PartiallyOrderedKnapsack model

docs/paper/reductions.typ

@@ -60,6 +60,7 @@
   "QUBO": [QUBO],
   "ILP": [Integer Linear Programming],
   "Knapsack": [Knapsack],
+  "PartiallyOrderedKnapsack": [Partially Ordered Knapsack],
   "Satisfiability": [SAT],
   "KSatisfiability": [$k$-SAT],
   "CircuitSAT": [CircuitSAT],
@@ -1164,6 +1165,14 @@ Biclique Cover is equivalent to factoring the biadjacency matrix $M$ of the bipa
   *Example.* Let $n = 4$ items with weights $(2, 3, 4, 5)$, values $(3, 4, 5, 7)$, and capacity $C = 7$. Selecting $S = {1, 2}$ (items with weights 3 and 4) gives total weight $3 + 4 = 7 lt.eq C$ and total value $4 + 5 = 9$. Selecting $S = {0, 3}$ (weights 2 and 5) gives weight $2 + 5 = 7 lt.eq C$ and value $3 + 7 = 10$, which is optimal.
 ]
 
+#problem-def("PartiallyOrderedKnapsack")[
+  Given a finite set $U$ with $|U| = n$ items, a partial order $<$ on $U$ (given by its cover relations), for each $u in U$ a size $s(u) in ZZ^+$ and a value $v(u) in ZZ^+$, and a capacity $B in ZZ^+$, find a downward-closed subset $U' subset.eq U$ (i.e., if $u in U'$ and $u' < u$ then $u' in U'$) maximizing $sum_(u in U') v(u)$ subject to $sum_(u in U') s(u) lt.eq B$.
+][
+  Garey and Johnson's problem A6 MP12 @garey1979. Unlike standard Knapsack, the partial order constraint makes the problem _strongly_ NP-complete --- it remains NP-complete even when $s(u) = v(u)$ for all $u$, so no pseudo-polynomial algorithm exists unless $P = N P$. The problem arises in manufacturing scheduling, project selection, and mining operations. For tree partial orders, Johnson and Niemi @johnson1983 gave pseudo-polynomial $O(n dot B)$ tree DP and an FPTAS. Kolliopoulos and Steiner @kolliopoulos2007 extended the FPTAS to 2-dimensional partial orders with $O(n^4 slash epsilon)$ running time.
+
+  *Example.* Consider $n = 6$ items with partial order given by cover relations $a < c$, $a < d$, $b < e$, $d < f$, $e < f$. Sizes $(2, 3, 4, 1, 2, 3)$, values $(3, 2, 5, 4, 3, 8)$, and capacity $B = 11$. Selecting $U' = {a, b, d, e, f}$ is downward-closed (all predecessors included), has total size $2 + 3 + 1 + 2 + 3 = 11 lt.eq B$, and total value $3 + 2 + 4 + 3 + 8 = 20$. Adding $c$ would exceed capacity ($15 > 11$).
+]
+
 #problem-def("RuralPostman")[
   Given an undirected graph $G = (V, E)$ with edge lengths $l: E -> ZZ_(gt.eq 0)$, a subset $E' subset.eq E$ of required edges, and a bound $B in ZZ^+$, determine whether there exists a circuit (closed walk) in $G$ that traverses every edge in $E'$ and has total length at most $B$.
 ][

docs/paper/references.bib

@@ -541,6 +541,28 @@ @article{cygan2014
   doi     = {10.1137/140990255}
 }
 
+@article{johnson1983,
+  author  = {David S. Johnson and Kenneth A. Niemi},
+  title   = {On Knapsacks, Partitions, and a New Dynamic Programming Technique for Trees},
+  journal = {Mathematics of Operations Research},
+  volume  = {8},
+  number  = {1},
+  pages   = {1--14},
+  year    = {1983},
+  doi     = {10.1287/moor.8.1.1}
+}
+
+@article{kolliopoulos2007,
+  author  = {Stavros G. Kolliopoulos and George Steiner},
+  title   = {Partially Ordered Knapsack and Applications to Scheduling},
+  journal = {Discrete Applied Mathematics},
+  volume  = {155},
+  number  = {8},
+  pages   = {889--897},
+  year    = {2007},
+  doi     = {10.1016/j.dam.2006.09.003}
+}
+
 @article{raiha1981,
   author  = {Kari-Jouko R{\"a}ih{\"a} and Esko Ukkonen},
   title   = {The Shortest Common Supersequence Problem over Binary Alphabet is {NP}-Complete},

docs/src/reductions/problem_schemas.json

@@ -488,6 +488,32 @@
       }
     ]
   },
+  {
+    "name": "PartiallyOrderedKnapsack",
+    "description": "Select items to maximize total value subject to precedence constraints and weight capacity",
+    "fields": [
+      {
+        "name": "sizes",
+        "type_name": "Vec<i64>",
+        "description": "Item sizes s(u) for each item"
+      },
+      {
+        "name": "values",
+        "type_name": "Vec<i64>",
+        "description": "Item values v(u) for each item"
+      },
+      {
+        "name": "precedences",
+        "type_name": "Vec<(usize, usize)>",
+        "description": "Precedence pairs (a, b) meaning a must be included before b"
+      },
+      {
+        "name": "capacity",
+        "type_name": "i64",
+        "description": "Knapsack capacity B"
+      }
+    ]
+  },
   {
     "name": "PartitionIntoTriangles",
     "description": "Partition vertices into triangles (K3 subgraphs)",

docs/src/reductions/reduction_graph.json

@@ -415,6 +415,13 @@
       "doc_path": "models/misc/struct.PaintShop.html",
       "complexity": "2^num_cars"
     },
+    {
+      "name": "PartiallyOrderedKnapsack",
+      "variant": {},
+      "category": "misc",
+      "doc_path": "models/misc/struct.PartiallyOrderedKnapsack.html",
+      "complexity": "2^num_items"
+    },
     {
       "name": "PartitionIntoTriangles",
       "variant": {
@@ -535,7 +542,7 @@
     },
     {
       "source": 4,
-      "target": 52,
+      "target": 53,
       "overhead": [
         {
           "field": "num_spins",
@@ -595,7 +602,7 @@
     },
     {
       "source": 11,
-      "target": 47,
+      "target": 48,
       "overhead": [
         {
           "field": "num_vars",
@@ -636,7 +643,7 @@
     },
     {
       "source": 18,
-      "target": 47,
+      "target": 48,
       "overhead": [
         {
           "field": "num_vars",
@@ -662,7 +669,7 @@
     },
     {
       "source": 19,
-      "target": 47,
+      "target": 48,
       "overhead": [
         {
           "field": "num_vars",
@@ -688,7 +695,7 @@
     },
     {
       "source": 20,
-      "target": 47,
+      "target": 48,
       "overhead": [
         {
           "field": "num_vars",
@@ -699,7 +706,7 @@
     },
     {
       "source": 20,
-      "target": 54,
+      "target": 55,
       "overhead": [
         {
           "field": "num_elements",
@@ -710,7 +717,7 @@
     },
     {
       "source": 21,
-      "target": 49,
+      "target": 50,
       "overhead": [
         {
           "field": "num_clauses",
@@ -729,7 +736,7 @@
     },
     {
       "source": 22,
-      "target": 47,
+      "target": 48,
       "overhead": [
         {
           "field": "num_vars",
@@ -755,7 +762,7 @@
     },
     {
       "source": 24,
-      "target": 52,
+      "target": 53,
       "overhead": [
         {
           "field": "num_spins",
@@ -1070,7 +1077,7 @@
     },
     {
       "source": 36,
-      "target": 47,
+      "target": 48,
       "overhead": [
         {
           "field": "num_vars",
@@ -1185,7 +1192,7 @@
       "doc_path": "rules/minimumvertexcover_minimumsetcovering/index.html"
     },
     {
-      "source": 47,
+      "source": 48,
       "target": 11,
       "overhead": [
         {
@@ -1200,8 +1207,8 @@
       "doc_path": "rules/qubo_ilp/index.html"
     },
     {
-      "source": 47,
-      "target": 51,
+      "source": 48,
+      "target": 52,
       "overhead": [
         {
           "field": "num_spins",
@@ -1211,7 +1218,7 @@
       "doc_path": "rules/spinglass_qubo/index.html"
     },
     {
-      "source": 49,
+      "source": 50,
       "target": 4,
       "overhead": [
         {
@@ -1226,7 +1233,7 @@
       "doc_path": "rules/sat_circuitsat/index.html"
     },
     {
-      "source": 49,
+      "source": 50,
       "target": 15,
       "overhead": [
         {
@@ -1241,7 +1248,7 @@
       "doc_path": "rules/sat_coloring/index.html"
     },
     {
-      "source": 49,
+      "source": 50,
       "target": 20,
       "overhead": [
         {
@@ -1256,7 +1263,7 @@
       "doc_path": "rules/sat_ksat/index.html"
     },
     {
-      "source": 49,
+      "source": 50,
       "target": 29,
       "overhead": [
         {
@@ -1271,7 +1278,7 @@
       "doc_path": "rules/sat_maximumindependentset/index.html"
     },
     {
-      "source": 49,
+      "source": 50,
       "target": 38,
       "overhead": [
         {
@@ -1286,8 +1293,8 @@
       "doc_path": "rules/sat_minimumdominatingset/index.html"
     },
     {
-      "source": 51,
-      "target": 47,
+      "source": 52,
+      "target": 48,
       "overhead": [
         {
           "field": "num_vars",
@@ -1297,7 +1304,7 @@
       "doc_path": "rules/spinglass_qubo/index.html"
     },
     {
-      "source": 52,
+      "source": 53,
       "target": 24,
       "overhead": [
         {
@@ -1312,8 +1319,8 @@
       "doc_path": "rules/spinglass_maxcut/index.html"
     },
     {
-      "source": 52,
-      "target": 51,
+      "source": 53,
+      "target": 52,
       "overhead": [
         {
           "field": "num_spins",
@@ -1327,7 +1334,7 @@
       "doc_path": "rules/spinglass_casts/index.html"
     },
     {
-      "source": 55,
+      "source": 56,
       "target": 11,
       "overhead": [
         {
@@ -1342,8 +1349,8 @@
       "doc_path": "rules/travelingsalesman_ilp/index.html"
     },
     {
-      "source": 55,
-      "target": 47,
+      "source": 56,
+      "target": 48,
       "overhead": [
         {
           "field": "num_vars",

problemreductions-cli/src/cli.rs

@@ -239,6 +239,7 @@ Flags by problem type:
   LCS                             --strings
   FAS                             --arcs [--weights] [--num-vertices]
   FVS                             --arcs [--weights] [--num-vertices]
+  PartiallyOrderedKnapsack        --sizes, --values, --capacity, --precedences
   FlowShopScheduling              --task-lengths, --deadline [--num-processors]
   SCS                             --strings, --bound [--alphabet-size]
   ILP, CircuitSAT                 (via reduction only)
@@ -382,6 +383,12 @@ pub struct CreateArgs {
     /// Directed arcs for directed graph problems (e.g., 0>1,1>2,2>0)
     #[arg(long)]
     pub arcs: Option<String>,
+    /// Item values (e.g., 3,4,5,7) for PartiallyOrderedKnapsack
+    #[arg(long)]
+    pub values: Option<String>,
+    /// Precedence pairs (e.g., "0>2,0>3,1>4") for PartiallyOrderedKnapsack
+    #[arg(long, alias = "item-precedences")]
+    pub precedences: Option<String>,
     /// Task lengths for FlowShopScheduling (semicolon-separated rows: "3,4,2;2,3,5;4,1,3")
     #[arg(long)]
     pub task_lengths: Option<String>,

problemreductions-cli/src/commands/create.rs

@@ -8,7 +8,7 @@ use problemreductions::export::{ModelExample, ProblemRef, ProblemSide, RuleExamp
 use problemreductions::models::algebraic::{ClosestVectorProblem, BMF};
 use problemreductions::models::graph::{GraphPartitioning, HamiltonianPath};
 use problemreductions::models::misc::{
-    BinPacking, FlowShopScheduling, LongestCommonSubsequence, PaintShop,
+    BinPacking, FlowShopScheduling, LongestCommonSubsequence, PaintShop, PartiallyOrderedKnapsack,
     ShortestCommonSupersequence, SubsetSum,
 };
 use problemreductions::prelude::*;
@@ -57,6 +57,8 @@ fn all_data_flags_empty(args: &CreateArgs) -> bool {
         && args.pattern.is_none()
         && args.strings.is_none()
         && args.arcs.is_none()
+        && args.values.is_none()
+        && args.precedences.is_none()
         && args.task_lengths.is_none()
         && args.deadline.is_none()
         && args.num_processors.is_none()
@@ -982,6 +984,52 @@ pub fn create(args: &CreateArgs, out: &OutputConfig) -> Result<()> {
             )
         }
 
+        // PartiallyOrderedKnapsack
+        "PartiallyOrderedKnapsack" => {
+            let sizes_str = args.sizes.as_deref().ok_or_else(|| {
+                anyhow::anyhow!(
+                    "PartiallyOrderedKnapsack requires --sizes, --values, and --capacity (--precedences is optional)\n\n\
+                     Usage: pred create PartiallyOrderedKnapsack --sizes 2,3,4,1,2,3 --values 3,2,5,4,3,8 --precedences \"0>2,0>3,1>4,3>5,4>5\" --capacity 11"
+                )
+            })?;
+            let values_str = args.values.as_deref().ok_or_else(|| {
+                anyhow::anyhow!("PartiallyOrderedKnapsack requires --values (e.g., 3,2,5,4,3,8)")
+            })?;
+            let cap_str = args.capacity.as_deref().ok_or_else(|| {
+                anyhow::anyhow!("PartiallyOrderedKnapsack requires --capacity (e.g., 11)")
+            })?;
+            let sizes: Vec<i64> = util::parse_comma_list(sizes_str)?;
+            let values: Vec<i64> = util::parse_comma_list(values_str)?;
+            let capacity: i64 = cap_str.parse()?;
+            let precedences = match args.precedences.as_deref() {
+                Some(s) if !s.trim().is_empty() => s
+                    .split(',')
+                    .map(|pair| {
+                        let parts: Vec<&str> = pair.trim().split('>').collect();
+                        anyhow::ensure!(
+                            parts.len() == 2,
+                            "Invalid precedence format '{}', expected 'a>b'",
+                            pair.trim()
+                        );
+                        Ok((
+                            parts[0].trim().parse::<usize>()?,
+                            parts[1].trim().parse::<usize>()?,
+                        ))
+                    })
+                    .collect::<Result<Vec<_>>>()?,
+                _ => vec![],
+            };
+            (
+                ser(PartiallyOrderedKnapsack::new(
+                    sizes,
+                    values,
+                    precedences,
+                    capacity,
+                ))?,
+                resolved_variant.clone(),
+            )
+        }
+
         _ => bail!("{}", crate::problem_name::unknown_problem_error(canonical)),
     };