Fix #215: [Model] EnsembleComputation (#721)

* Add plan for #215: [Model] EnsembleComputation

* Implement #215: [Model] EnsembleComputation

* chore: remove plan file after implementation

---------

Co-authored-by: Xiwei Pan <xiwei.pan@connect.hkust-gz.edu.cn>
Co-authored-by: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

Author: 3 people

docs/paper/reductions.typ

@@ -98,6 +98,7 @@
   "KSatisfiability": [$k$-SAT],
   "CircuitSAT": [CircuitSAT],
   "ConjunctiveQueryFoldability": [Conjunctive Query Foldability],
+  "EnsembleComputation": [Ensemble Computation],
   "Factoring": [Factoring],
   "KingsSubgraph": [King's Subgraph MIS],
   "TriangularSubgraph": [Triangular Subgraph MIS],
@@ -2627,6 +2628,56 @@ A classical NP-complete problem from Garey and Johnson @garey1979[Ch.~3, p.~76],
   ) <fig:cqf-example>
 ]
 
+#problem-def("EnsembleComputation")[
+  Given a finite set $A$, a collection $C$ of subsets of $A$, and a positive integer $J$, determine whether there exists a sequence $S = (z_1 <- x_1 union y_1, z_2 <- x_2 union y_2, dots, z_j <- x_j union y_j)$ of $j <= J$ union operations such that each operand $x_i, y_i$ is either a singleton ${a}$ for some $a in A$ or a previously computed set $z_k$ with $k < i$, the two operands are disjoint for every step, and every target subset $c in C$ is equal to some computed set $z_i$.
+][
+  Ensemble Computation is problem PO9 in Garey and Johnson @garey1979. It can be viewed as monotone circuit synthesis over set union: each operation introduces one reusable intermediate set, and the objective is simply to realize all targets within the given budget. The implementation in this library uses $2J$ operand variables with domain size $|A| + J$ and accepts as soon as some valid prefix has produced every target set, so the original "$j <= J$" semantics are preserved under brute-force enumeration. The resulting search space yields a straightforward exact upper bound of $(|A| + J)^(2J)$. Järvisalo, Kaski, Koivisto, and Korhonen study SAT encodings for finding efficient ensemble computations in a monotone-circuit setting @jarvisalo2012.
+
+  *Example.* Let $A = {0, 1, 2, 3}$, $C = {{0, 1, 2}, {0, 1, 3}}$, and $J = 4$. A satisfying witness uses three essential unions:
+  $z_1 = {0} union {1} = {0, 1}$,
+  $z_2 = z_1 union {2} = {0, 1, 2}$, and
+  $z_3 = z_1 union {3} = {0, 1, 3}$.
+  Thus both target subsets appear among the computed $z_i$ values while staying within the budget.
+
+  #figure(
+    canvas(length: 1cm, {
+      import draw: *
+      let node(pos, label, name, fill) = {
+        rect(
+          (pos.at(0) - 0.45, pos.at(1) - 0.18),
+          (pos.at(0) + 0.45, pos.at(1) + 0.18),
+          radius: 0.08,
+          fill: fill,
+          stroke: 0.5pt + luma(140),
+          name: name,
+        )
+        content(name, text(7pt, label))
+      }
+
+      let base = rgb("#4e79a7").transparentize(78%)
+      let target = rgb("#59a14f").transparentize(72%)
+      let aux = rgb("#f28e2b").transparentize(74%)
+
+      node((0.0, 1.4), [\{0\}], "a0", base)
+      node((1.2, 1.4), [\{1\}], "a1", base)
+      node((2.4, 1.4), [\{2\}], "a2", base)
+      node((3.6, 1.4), [\{3\}], "a3", base)
+
+      node((0.6, 0.6), [$z_1 = \{0,1\}$], "z1", aux)
+      node((1.8, -0.2), [$z_2 = \{0,1,2\}$], "z2", target)
+      node((3.0, -0.2), [$z_3 = \{0,1,3\}$], "z3", target)
+
+      line("a0.south", "z1.north-west", stroke: 0.5pt + luma(120), mark: (end: "straight", scale: 0.4))
+      line("a1.south", "z1.north-east", stroke: 0.5pt + luma(120), mark: (end: "straight", scale: 0.4))
+      line("z1.south-west", "z2.north-west", stroke: 0.5pt + luma(120), mark: (end: "straight", scale: 0.4))
+      line("a2.south", "z2.north-east", stroke: 0.5pt + luma(120), mark: (end: "straight", scale: 0.4))
+      line("z1.south-east", "z3.north-west", stroke: 0.5pt + luma(120), mark: (end: "straight", scale: 0.4))
+      line("a3.south", "z3.north-east", stroke: 0.5pt + luma(120), mark: (end: "straight", scale: 0.4))
+    }),
+    caption: [An ensemble computation for $A = {0,1,2,3}$ and $C = {{0,1,2}, {0,1,3}}$. The intermediate set $z_1 = {0,1}$ is reused to produce both target subsets.],
+  ) <fig:ensemble-computation>
+]
+
 #{
   let x = load-model-example("Factoring")
   let N = x.instance.target

docs/paper/references.bib

@@ -504,6 +504,18 @@ @article{bjorklund2009
   doi     = {10.1137/070683933}
 }
 
+@incollection{jarvisalo2012,
+  author    = {Matti J\"{a}rvisalo and Petteri Kaski and Mikko Koivisto and Janne H. Korhonen},
+  title     = {Finding Efficient Circuits for Ensemble Computation},
+  booktitle = {Theory and Applications of Satisfiability Testing -- SAT 2012},
+  series    = {Lecture Notes in Computer Science},
+  volume    = {7317},
+  pages     = {369--382},
+  year      = {2012},
+  publisher = {Springer},
+  doi       = {10.1007/978-3-642-31612-8_28}
+}
+
 @article{aspvall1979,
   author  = {Bengt Aspvall and Michael F. Plass and Robert Endre Tarjan},
   title   = {A Linear-Time Algorithm for Testing the Truth of Certain Quantified Boolean Formulas},

problemreductions-cli/src/cli.rs

@@ -244,6 +244,7 @@ Flags by problem type:
   MaximumSetPacking               --sets [--weights]
   MinimumHittingSet               --universe, --sets
   MinimumSetCovering              --universe, --sets [--weights]
+  EnsembleComputation             --universe, --sets, --budget
   ComparativeContainment          --universe, --r-sets, --s-sets [--r-weights] [--s-weights]
   X3C (ExactCoverBy3Sets)         --universe, --sets (3 elements each)
   SetBasis                        --universe, --sets, --k

problemreductions-cli/src/commands/create.rs

@@ -18,9 +18,9 @@ use problemreductions::models::graph::{
 };
 use problemreductions::models::misc::{
     AdditionalKey, BinPacking, BoyceCoddNormalFormViolation, CbqRelation, ConjunctiveBooleanQuery,
-    ConsistencyOfDatabaseFrequencyTables, FlowShopScheduling, FrequencyTable, KnownValue,
-    LongestCommonSubsequence, MinimumTardinessSequencing, MultiprocessorScheduling, PaintShop,
-    PartiallyOrderedKnapsack, QueryArg, RectilinearPictureCompression,
+    ConsistencyOfDatabaseFrequencyTables, EnsembleComputation, FlowShopScheduling, FrequencyTable,
+    KnownValue, LongestCommonSubsequence, MinimumTardinessSequencing, MultiprocessorScheduling,
+    PaintShop, PartiallyOrderedKnapsack, QueryArg, RectilinearPictureCompression,
     ResourceConstrainedScheduling, SchedulingWithIndividualDeadlines,
     SequencingToMinimizeMaximumCumulativeCost, SequencingToMinimizeWeightedCompletionTime,
     SequencingToMinimizeWeightedTardiness, SequencingWithReleaseTimesAndDeadlines,
@@ -498,6 +498,7 @@ fn type_format_hint(type_name: &str, graph_type: Option<&str>) -> &'static str {
 
 fn cli_flag_name(field_name: &str) -> String {
     match field_name {
+        "universe_size" => "universe".to_string(),
         "vertex_weights" => "weights".to_string(),
         "edge_lengths" => "edge-weights".to_string(),
         _ => field_name.replace('_', "-"),
@@ -554,6 +555,7 @@ fn example_for(canonical: &str, graph_type: Option<&str>) -> &'static str {
         "SpinGlass" => "--graph 0-1,1-2 --couplings 1,1",
         "KColoring" => "--graph 0-1,1-2,2-0 --k 3",
         "HamiltonianCircuit" => "--graph 0-1,1-2,2-3,3-0",
+        "EnsembleComputation" => "--universe 4 --sets \"0,1,2;0,1,3\" --budget 4",
         "MinMaxMulticenter" => {
             "--graph 0-1,1-2,2-3 --weights 1,1,1,1 --edge-weights 1,1,1 --k 2 --bound 2"
         }
@@ -1992,6 +1994,31 @@ pub fn create(args: &CreateArgs, out: &OutputConfig) -> Result<()> {
             )
         }
 
+        // EnsembleComputation
+        "EnsembleComputation" => {
+            let usage =
+                "Usage: pred create EnsembleComputation --universe 4 --sets \"0,1,2;0,1,3\" --budget 4";
+            let universe_size = args.universe.ok_or_else(|| {
+                anyhow::anyhow!("EnsembleComputation requires --universe\n\n{usage}")
+            })?;
+            let subsets = parse_sets(args)?;
+            let budget = args
+                .budget
+                .as_deref()
+                .ok_or_else(|| anyhow::anyhow!("EnsembleComputation requires --budget\n\n{usage}"))?
+                .parse::<usize>()
+                .map_err(|e| {
+                    anyhow::anyhow!(
+                        "Invalid --budget value for EnsembleComputation: {e}\n\n{usage}"
+                    )
+                })?;
+            (
+                ser(EnsembleComputation::try_new(universe_size, subsets, budget)
+                    .map_err(anyhow::Error::msg)?)?,
+                resolved_variant.clone(),
+            )
+        }
+
         // ComparativeContainment
         "ComparativeContainment" => {
             let universe = args.universe.ok_or_else(|| {
@@ -5826,6 +5853,37 @@ mod tests {
         std::fs::remove_file(output_path).ok();
     }
 
+    #[test]
+    fn test_create_ensemble_computation_json() {
+        let mut args = empty_args();
+        args.problem = Some("EnsembleComputation".to_string());
+        args.universe = Some(4);
+        args.sets = Some("0,1,2;0,1,3".to_string());
+        args.budget = Some("4".to_string());
+
+        let output_path = std::env::temp_dir().join("pred_test_create_ensemble_computation.json");
+        let out = OutputConfig {
+            output: Some(output_path.clone()),
+            quiet: true,
+            json: false,
+            auto_json: false,
+        };
+
+        create(&args, &out).unwrap();
+
+        let content = std::fs::read_to_string(&output_path).unwrap();
+        let json: serde_json::Value = serde_json::from_str(&content).unwrap();
+        assert_eq!(json["type"], "EnsembleComputation");
+        assert_eq!(json["data"]["universe_size"], 4);
+        assert_eq!(
+            json["data"]["subsets"],
+            serde_json::json!([[0, 1, 2], [0, 1, 3]])
+        );
+        assert_eq!(json["data"]["budget"], 4);
+
+        std::fs::remove_file(output_path).ok();
+    }
+
     #[test]
     fn test_create_balanced_complete_bipartite_subgraph() {
         use crate::dispatch::ProblemJsonOutput;

problemreductions-cli/tests/cli_tests.rs

@@ -7335,6 +7335,97 @@ fn test_create_sequencing_within_intervals() {
     std::fs::remove_file(&output_file).ok();
 }
 
+#[test]
+fn test_create_ensemble_computation() {
+    let output_file = std::env::temp_dir().join("pred_test_create_ensemble_computation.json");
+    let output = pred()
+        .args([
+            "-o",
+            output_file.to_str().unwrap(),
+            "create",
+            "EnsembleComputation",
+            "--universe",
+            "4",
+            "--sets",
+            "0,1,2;0,1,3",
+            "--budget",
+            "4",
+        ])
+        .output()
+        .unwrap();
+    assert!(
+        output.status.success(),
+        "stderr: {}",
+        String::from_utf8_lossy(&output.stderr)
+    );
+    let content = std::fs::read_to_string(&output_file).unwrap();
+    let json: serde_json::Value = serde_json::from_str(&content).unwrap();
+    assert_eq!(json["type"], "EnsembleComputation");
+    assert_eq!(json["data"]["universe_size"], 4);
+    assert_eq!(
+        json["data"]["subsets"],
+        serde_json::json!([[0, 1, 2], [0, 1, 3]])
+    );
+    assert_eq!(json["data"]["budget"], 4);
+    std::fs::remove_file(&output_file).ok();
+}
+
+#[test]
+fn test_create_ensemble_computation_no_flags_uses_cli_flag_names() {
+    let output = pred()
+        .args(["create", "EnsembleComputation"])
+        .output()
+        .unwrap();
+    assert!(
+        !output.status.success(),
+        "problem-specific help should exit non-zero"
+    );
+    let stderr = String::from_utf8_lossy(&output.stderr);
+    assert!(
+        stderr.contains("--universe"),
+        "expected --universe in help, got: {stderr}"
+    );
+    assert!(
+        stderr.contains("--sets"),
+        "expected --sets in help, got: {stderr}"
+    );
+    assert!(
+        stderr.contains("--budget"),
+        "expected --budget in help, got: {stderr}"
+    );
+    assert!(
+        !stderr.contains("--universe-size"),
+        "help should use actual CLI flags, got: {stderr}"
+    );
+}
+
+#[test]
+fn test_create_ensemble_computation_rejects_out_of_range_elements_without_panicking() {
+    let output = pred()
+        .args([
+            "create",
+            "EnsembleComputation",
+            "--universe",
+            "4",
+            "--sets",
+            "0,1,5",
+            "--budget",
+            "4",
+        ])
+        .output()
+        .unwrap();
+    assert!(!output.status.success());
+    let stderr = String::from_utf8_lossy(&output.stderr);
+    assert!(
+        !stderr.contains("panicked at"),
+        "expected graceful CLI error, got panic: {stderr}"
+    );
+    assert!(
+        stderr.contains("outside universe") || stderr.contains("universe of size"),
+        "expected out-of-range subset error, got: {stderr}"
+    );
+}
+
 #[test]
 fn test_create_scheduling_with_individual_deadlines_with_m_alias() {
     let output_file =
@@ -7483,6 +7574,22 @@ fn test_create_model_example_sequencing_within_intervals() {
     assert_eq!(json["type"], "SequencingWithinIntervals");
 }
 
+#[test]
+fn test_create_model_example_ensemble_computation() {
+    let output = pred()
+        .args(["create", "--example", "EnsembleComputation"])
+        .output()
+        .unwrap();
+    assert!(
+        output.status.success(),
+        "stderr: {}",
+        String::from_utf8_lossy(&output.stderr)
+    );
+    let stdout = String::from_utf8(output.stdout).unwrap();
+    let json: serde_json::Value = serde_json::from_str(&stdout).unwrap();
+    assert_eq!(json["type"], "EnsembleComputation");
+}
+
 #[test]
 fn test_create_minimum_multiway_cut_rejects_single_terminal() {
     let output = pred()

src/lib.rs

@@ -66,7 +66,7 @@ pub mod prelude {
     pub use crate::models::misc::{
         AdditionalKey, BinPacking, BoyceCoddNormalFormViolation, CbqRelation,
         ConjunctiveBooleanQuery, ConjunctiveQueryFoldability, ConsistencyOfDatabaseFrequencyTables,
-        Factoring, FlowShopScheduling, Knapsack, LongestCommonSubsequence,
+        EnsembleComputation, Factoring, FlowShopScheduling, Knapsack, LongestCommonSubsequence,
         MinimumTardinessSequencing, MultiprocessorScheduling, PaintShop, Partition, QueryArg,
         RectilinearPictureCompression, ResourceConstrainedScheduling,
         SchedulingWithIndividualDeadlines, SequencingToMinimizeMaximumCumulativeCost,