Fix #639: [Rule] Knapsack to ILP by GiggleLiu · Pull Request #688 · CodingThrust/problem-reductions

GiggleLiu · 2026-03-16T20:19:58Z

Summary

add an implementation plan for the Knapsack to ILP reduction
prepare issue [Rule] Knapsack to ILP #639 for autonomous execution

Fixes #639

GiggleLiu · 2026-03-16T20:42:37Z

Implementation Summary

Changes

Added the direct Knapsack -> ILP rule in src/rules/knapsack_ilp.rs, including the canonical issue example and identity solution extraction for the binary ILP formulation.
Registered the new rule and updated tests so the reduction graph now expects the direct Knapsack -> ILP edge, while the dominated-rule allow-list now includes the existing Knapsack -> QUBO rule because it is dominated by Knapsack -> ILP -> QUBO.
Added the paper entry and citation for the reduction, and regenerated the canonical example fixture so examples.json includes the new Knapsack -> ILP example.
Tightened rule tests with an empty-instance case and an exact canonical-example witness assertion.

Deviations from Plan

None.

Open Questions

None.

Copilot

Pull request overview

Implements and documents a new direct reduction rule from Knapsack to ILP (binary), connecting Knapsack into the ILP-centered reduction graph and adding corresponding tests and example-db fixtures.

Changes:

Add Knapsack -> ILP<bool> reduction rule with canonical example spec registration.
Add unit tests validating closed-loop correctness, ILP structure, and reduction-graph reachability; update dominated-rule expectations.
Update example-db fixtures and paper docs to include the new Knapsack→ILP canonical example and citation.

Reviewed changes

Copilot reviewed 8 out of 8 changed files in this pull request and generated 4 comments.

Show a summary per file

File	Description
`src/rules/knapsack_ilp.rs`	New Knapsack→ILP reduction implementation + example-db spec + tests module hook
`src/rules/mod.rs`	Registers the new rule module and its canonical example specs under `ilp-solver`
`src/unit_tests/rules/knapsack_ilp.rs`	New unit tests for reduction correctness/structure and example-db spec
`src/unit_tests/rules/graph.rs`	Adds a reduction-graph path test asserting direct Knapsack→ILP step exists
`src/unit_tests/rules/analysis.rs`	Updates dominated-rule allow-list to include Knapsack→QUBO dominated via Knapsack→ILP→QUBO
`src/example_db/fixtures/examples.json`	Adds Knapsack→ILP fixture; also includes broader fixture updates
`docs/paper/references.bib`	Adds Papadimitriou & Steiglitz (1982) book reference
`docs/paper/reductions.typ`	Adds paper section describing Knapsack→ILP reduction with a loaded canonical example

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src/example_db/fixtures/examples.json

    {"source":{"problem":"KSatisfiability","variant":{"k":"K2"},"instance":{"clauses":[{"literals":[1,2]},{"literals":[-1,3]},{"literals":[-2,4]},{"literals":[-3,-4]}],"num_vars":4}},"target":{"problem":"QUBO","variant":{"weight":"f64"},"instance":{"matrix":[[0.0,1.0,-1.0,0.0],[0.0,0.0,0.0,-1.0],[0.0,0.0,0.0,1.0],[0.0,0.0,0.0,0.0]],"num_vars":4}},"solutions":[{"source_config":[0,1,0,1],"target_config":[0,1,0,1]}]},
-    {"source":{"problem":"KSatisfiability","variant":{"k":"K3"},"instance":{"clauses":[{"literals":[1,2,-3]},{"literals":[-1,3,4]},{"literals":[2,-4,5]},{"literals":[-2,3,-5]},{"literals":[1,-3,5]},{"literals":[-1,-2,4]},{"literals":[3,-4,-5]}],"num_vars":5}},"target":{"problem":"QUBO","variant":{"weight":"f64"},"instance":{"matrix":[[0.0,4.0,-4.0,0.0,0.0,4.0,-4.0,0.0,0.0,4.0,-4.0,0.0],[0.0,0.0,-2.0,-2.0,0.0,4.0,0.0,4.0,-4.0,0.0,-4.0,0.0],[0.0,0.0,2.0,-2.0,0.0,1.0,4.0,0.0,4.0,-4.0,0.0,4.0],[0.0,0.0,0.0,4.0,0.0,0.0,-1.0,-4.0,0.0,0.0,-1.0,-4.0],[0.0,0.0,0.0,0.0,0.0,0.0,0.0,-1.0,1.0,-1.0,0.0,1.0],[0.0,0.0,0.0,0.0,0.0,-2.0,0.0,0.0,0.0,0.0,0.0,0.0],[0.0,0.0,0.0,0.0,0.0,0.0,3.0,0.0,0.0,0.0,0.0,0.0],[0.0,0.0,0.0,0.0,0.0,0.0,0.0,3.0,0.0,0.0,0.0,0.0],[0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,2.0,0.0,0.0,0.0],[0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,3.0,0.0,0.0],[0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,7.0,0.0],[0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,2.0]],"num_vars":12}},"solutions":[{"source_config":[0,0,0,0,0],"target_config":[0,0,0,0,0,1,0,0,0,0,0,0]}]},
+    {"source":{"problem":"KSatisfiability","variant":{"k":"K3"},"instance":{"clauses":[{"literals":[1,2,-3]},{"literals":[-1,3,4]},{"literals":[2,-4,5]},{"literals":[-2,3,-5]},{"literals":[1,-3,5]},{"literals":[-1,-2,4]},{"literals":[3,-4,-5]}],"num_vars":5}},"target":{"problem":"QUBO","variant":{"weight":"f64"},"instance":{"matrix":[[0.0,4.0,-4.0,0.0,0.0,4.0,-4.0,0.0,0.0,4.0,-4.0,0.0],[0.0,0.0,-2.0,-2.0,0.0,4.0,0.0,4.0,-4.0,0.0,-4.0,0.0],[0.0,0.0,2.0,-2.0,0.0,1.0,4.0,0.0,4.0,-4.0,0.0,4.0],[0.0,0.0,0.0,4.0,0.0,0.0,-1.0,-4.0,0.0,0.0,-1.0,-4.0],[0.0,0.0,0.0,0.0,0.0,0.0,0.0,-1.0,1.0,-1.0,0.0,1.0],[0.0,0.0,0.0,0.0,0.0,-2.0,0.0,0.0,0.0,0.0,0.0,0.0],[0.0,0.0,0.0,0.0,0.0,0.0,3.0,0.0,0.0,0.0,0.0,0.0],[0.0,0.0,0.0,0.0,0.0,0.0,0.0,3.0,0.0,0.0,0.0,0.0],[0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,2.0,0.0,0.0,0.0],[0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,3.0,0.0,0.0],[0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,7.0,0.0],[0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,2.0]],"num_vars":12}},"solutions":[{"source_config":[1,1,1,1,1],"target_config":[1,1,1,1,1,0,0,0,0,0,1,0]}]},
    {"source":{"problem":"KSatisfiability","variant":{"k":"K3"},"instance":{"clauses":[{"literals":[1,2,3]},{"literals":[-1,-2,3]}],"num_vars":3}},"target":{"problem":"SubsetSum","variant":{},"instance":{"sizes":["10010","10001","1010","1001","111","100","10","20","1","2"],"target":"11144"}},"solutions":[{"source_config":[0,0,1],"target_config":[0,1,0,1,1,0,1,1,1,0]}]},
    {"source":{"problem":"KSatisfiability","variant":{"k":"KN"},"instance":{"clauses":[{"literals":[1,-2,3]},{"literals":[-1,3,4]},{"literals":[2,-3,-4]}],"num_vars":4}},"target":{"problem":"Satisfiability","variant":{},"instance":{"clauses":[{"literals":[1,-2,3]},{"literals":[-1,3,4]},{"literals":[2,-3,-4]}],"num_vars":4}},"solutions":[{"source_config":[1,1,1,0],"target_config":[1,1,1,0]}]},
+    {"source":{"problem":"Knapsack","variant":{},"instance":{"capacity":7,"values":[1,4,5,7],"weights":[1,3,4,5]}},"target":{"problem":"ILP","variant":{"variable":"bool"},"instance":{"constraints":[{"cmp":"Le","rhs":7.0,"terms":[[0,1.0],[1,3.0],[2,4.0],[3,5.0]]}],"num_vars":4,"objective":[[0,1.0],[1,4.0],[2,5.0],[3,7.0]],"sense":"Maximize"}},"solutions":[{"source_config":[0,1,1,0],"target_config":[0,1,1,0]}]},
    {"source":{"problem":"Knapsack","variant":{},"instance":{"capacity":7,"values":[3,4,5,7],"weights":[2,3,4,5]}},"target":{"problem":"QUBO","variant":{"weight":"f64"},"instance":{"matrix":[[-483.0,240.0,320.0,400.0,80.0,160.0,320.0],[0.0,-664.0,480.0,600.0,120.0,240.0,480.0],[0.0,0.0,-805.0,800.0,160.0,320.0,640.0],[0.0,0.0,0.0,-907.0,200.0,400.0,800.0],[0.0,0.0,0.0,0.0,-260.0,80.0,160.0],[0.0,0.0,0.0,0.0,0.0,-480.0,320.0],[0.0,0.0,0.0,0.0,0.0,0.0,-800.0]],"num_vars":7}},"solutions":[{"source_config":[1,0,0,1],"target_config":[1,0,0,1,0,0,0]}]},
    {"source":{"problem":"LongestCommonSubsequence","variant":{},"instance":{"strings":[[65,66,65,67],[66,65,67,65]]}},"target":{"problem":"ILP","variant":{"variable":"bool"},"instance":{"constraints":[{"cmp":"Le","rhs":1.0,"terms":[[0,1.0],[1,1.0]]},{"cmp":"Le","rhs":1.0,"terms":[[2,1.0]]},{"cmp":"Le","rhs":1.0,"terms":[[3,1.0],[4,1.0]]},{"cmp":"Le","rhs":1.0,"terms":[[5,1.0]]},{"cmp":"Le","rhs":1.0,"terms":[[2,1.0]]},{"cmp":"Le","rhs":1.0,"terms":[[0,1.0],[3,1.0]]},{"cmp":"Le","rhs":1.0,"terms":[[5,1.0]]},{"cmp":"Le","rhs":1.0,"terms":[[1,1.0],[4,1.0]]},{"cmp":"Le","rhs":1.0,"terms":[[0,1.0],[2,1.0]]},{"cmp":"Le","rhs":1.0,"terms":[[1,1.0],[2,1.0]]},{"cmp":"Le","rhs":1.0,"terms":[[1,1.0],[3,1.0]]},{"cmp":"Le","rhs":1.0,"terms":[[1,1.0],[5,1.0]]},{"cmp":"Le","rhs":1.0,"terms":[[4,1.0],[5,1.0]]}],"num_vars":6,"objective":[[0,1.0],[1,1.0],[2,1.0],[3,1.0],[4,1.0],[5,1.0]],"sense":"Maximize"}},"solutions":[{"source_config":[0,1,1,1],"target_config":[0,0,1,1,0,1]}]},
-    {"source":{"problem":"MaxCut","variant":{"graph":"SimpleGraph","weight":"i32"},"instance":{"edge_weights":[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],"graph":{"inner":{"edge_property":"undirected","edges":[[0,1,null],[0,4,null],[0,5,null],[1,2,null],[1,6,null],[2,3,null],[2,7,null],[3,4,null],[3,8,null],[4,9,null],[5,7,null],[5,8,null],[6,8,null],[6,9,null],[7,9,null]],"node_holes":[],"nodes":[null,null,null,null,null,null,null,null,null,null]}}}},"target":{"problem":"SpinGlass","variant":{"graph":"SimpleGraph","weight":"i32"},"instance":{"couplings":[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],"fields":[0,0,0,0,0,0,0,0,0,0],"graph":{"inner":{"edge_property":"undirected","edges":[[0,1,null],[0,4,null],[0,5,null],[1,2,null],[1,6,null],[2,3,null],[2,7,null],[3,4,null],[3,8,null],[4,9,null],[5,7,null],[5,8,null],[6,8,null],[6,9,null],[7,9,null]],"node_holes":[],"nodes":[null,null,null,null,null,null,null,null,null,null]}}}},"solutions":[{"source_config":[0,1,0,1,0,1,0,0,0,1],"target_config":[0,1,0,1,0,1,0,0,0,1]}]},
+    {"source":{"problem":"MaxCut","variant":{"graph":"SimpleGraph","weight":"i32"},"instance":{"edge_weights":[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],"graph":{"inner":{"edge_property":"undirected","edges":[[0,1,null],[0,4,null],[0,5,null],[1,2,null],[1,6,null],[2,3,null],[2,7,null],[3,4,null],[3,8,null],[4,9,null],[5,7,null],[5,8,null],[6,8,null],[6,9,null],[7,9,null]],"node_holes":[],"nodes":[null,null,null,null,null,null,null,null,null,null]}}}},"target":{"problem":"SpinGlass","variant":{"graph":"SimpleGraph","weight":"i32"},"instance":{"couplings":[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],"fields":[0,0,0,0,0,0,0,0,0,0],"graph":{"inner":{"edge_property":"undirected","edges":[[0,1,null],[0,4,null],[0,5,null],[1,2,null],[1,6,null],[2,3,null],[2,7,null],[3,4,null],[3,8,null],[4,9,null],[5,7,null],[5,8,null],[6,8,null],[6,9,null],[7,9,null]],"node_holes":[],"nodes":[null,null,null,null,null,null,null,null,null,null]}}}},"solutions":[{"source_config":[1,0,1,0,0,0,0,0,1,1],"target_config":[1,0,1,0,0,0,0,0,1,1]}]},
    {"source":{"problem":"MaximumClique","variant":{"graph":"SimpleGraph","weight":"i32"},"instance":{"graph":{"inner":{"edge_property":"undirected","edges":[[0,1,null],[0,2,null],[0,3,null],[0,4,null],[1,2,null],[1,3,null],[1,5,null],[2,4,null],[2,5,null],[3,4,null],[3,5,null],[4,5,null]],"node_holes":[],"nodes":[null,null,null,null,null,null]}},"weights":[1,1,1,1,1,1]}},"target":{"problem":"ILP","variant":{"variable":"bool"},"instance":{"constraints":[{"cmp":"Le","rhs":1.0,"terms":[[0,1.0],[5,1.0]]},{"cmp":"Le","rhs":1.0,"terms":[[1,1.0],[4,1.0]]},{"cmp":"Le","rhs":1.0,"terms":[[2,1.0],[3,1.0]]}],"num_vars":6,"objective":[[0,1.0],[1,1.0],[2,1.0],[3,1.0],[4,1.0],[5,1.0]],"sense":"Maximize"}},"solutions":[{"source_config":[1,1,1,0,0,0],"target_config":[1,1,1,0,0,0]}]},


src/unit_tests/rules/analysis.rs

        ("Factoring", "ILP {variable: \"i32\"}"),
        // K3-SAT → QUBO via SAT → CircuitSAT → SpinGlass chain
        ("KSatisfiability {k: \"K3\"}", "QUBO {weight: \"f64\"}"),
+        // Knapsack -> ILP -> QUBO is better than the direct penalty reduction
+        ("Knapsack", "QUBO {weight: \"f64\"}"),
        // MaxMatching → MaxSetPacking → ILP is better than direct MaxMatching → ILP


src/rules/knapsack_ilp.rs

+//! Reduction from Knapsack to ILP (Integer Linear Programming).
+//!
+//! The standard 0-1 knapsack formulation is already a binary ILP:
+//! - Variables: one binary variable per item
+//! - Constraint: the total selected weight must not exceed capacity
+//! - Objective: maximize the total selected value
+


src/unit_tests/rules/graph.rs

+#[test]
+fn test_knapsack_to_ilp_path_exists() {
+    let graph = ReductionGraph::new();
+    let src = ReductionGraph::variant_to_map(&Knapsack::variant());
+    let dst = ReductionGraph::variant_to_map(&ILP::<bool>::variant());
+    let path = graph.find_cheapest_path(
+        "Knapsack",
+        &src,
+        "ILP",
+        &dst,
+        &ProblemSize::new(vec![]),
+        &MinimizeSteps,
+    );
+
+    let path = path.expect("Knapsack should reduce to ILP");
+    assert_eq!(
+        path.type_names(),
+        vec!["Knapsack", "ILP"],
+        "Knapsack should have a direct ILP reduction"
+    );
+    assert_eq!(path.len(), 1, "Knapsack -> ILP should be one direct step");
+}


codecov · 2026-03-16T23:30:29Z

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 97.48%. Comparing base (7906394) to head (91345cf).
⚠️ Report is 1 commits behind head on main.

Additional details and impacted files

@@           Coverage Diff            @@
##             main     #688    +/-   ##
========================================
  Coverage   97.47%   97.48%            
========================================
  Files         355      357     +2     
  Lines       45294    45418   +124     
========================================
+ Hits        44151    44274   +123     
- Misses       1143     1144     +1

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GiggleLiu · 2026-03-18T19:59:57Z

Agentic Review Report

Structural Check

#	Check	Status
1	Rule file exists (`src/rules/knapsack_ilp.rs`)	PASS
2	`#[reduction(...)]` macro present	PASS
3	`ReductionResult` impl present	PASS
4	`ReduceTo` impl present	PASS
5	`#[cfg(test)]` + `#[path = "..."]` test link	PASS
6	Test file exists (`src/unit_tests/rules/knapsack_ilp.rs`)	PASS
7	Closed-loop test present (`test_knapsack_to_ilp_closed_loop`)	PASS
8	Registered in `rules/mod.rs`	PASS
9	Canonical rule example registered	PASS
10	Example-db lookup tests exist	PASS
11	Paper `reduction-rule` entry	PASS

Build: make test PASS, make clippy PASS

Semantic Review:

reduce_to() correctness: OK — Standard textbook mapping: n binary ILP variables, single capacity constraint, value-maximization objective. Traced with canonical example (4 items, weights=[1,3,4,5], values=[1,4,5,7], capacity=7 → optimal [0,1,1,0], value=9). Correct.
extract_solution correctness: OK — Identity mapping (1-to-1 Knapsack↔ILP variables).
Overhead accuracy: OK — num_vars = "num_items" (verified: ILP constructed with num_vars = self.num_items()), num_constraints = "1" (verified: exactly one capacity inequality).
Paper proof sketch: OK — Forward and backward correctness arguments present. Sound and valid.
No duplicate registrations: OK — Single ReduceTo<ILP<bool>> for Knapsack impl.
Dominated rule update: OK — analysis.rs correctly adds ("Knapsack", "QUBO {weight: \"f64\"}") to known dominated set (Knapsack→ILP→QUBO now dominates direct Knapsack→QUBO).

Issue Compliance: 6/6 passed (source/target, algorithm, solution extraction, correctness, overhead, example all match issue #639).

Quality Check

Design Principles:

DRY: OK — Follows same structural pattern as other ILP reductions without copy-pasting. Identity extract_solution is a one-liner shared pattern.
KISS: OK — reduce_to() is 18 lines doing exactly one thing. No over-engineering.
HC/LC: OK — Single responsibility maintained throughout.

HCI: Not applicable (no CLI/MCP code changed).

Test Quality:

5 dedicated tests: closed-loop round-trip, ILP structure validation (7 assertions), zero-capacity edge case, empty-instance edge case, canonical example spec validation.
Plus: graph path test in graph.rs, dominated-rules analysis update in analysis.rs.
All tests use meaningful assertions, not shape-only checks.

Issues:

#	Severity	Finding	Location
Q1	Minor	`i64 as f64` cast can lose precision for values >2^53. Consistent with codebase conventions but Knapsack uses `i64` (wider range than `i32` in other ILP reductions).	`src/rules/knapsack_ilp.rs:47,49,55`
Q2	Minor	Only one non-trivial closed-loop test instance. Boundary tests add coverage, but a second 5+ item instance would strengthen confidence.	`src/unit_tests/rules/knapsack_ilp.rs:8`

Agentic Feature Tests

Test Environment: PR #688 branch, debug + release builds tested.

Test	Status	Severity
Catalog listing (`pred list`)	Knapsack→ILP missing from catalog	critical
Problem details (`pred show Knapsack`)	Only shows QUBO reduction, ILP absent	critical
ILP incoming (`pred show ILP`)	11 incoming reductions listed, Knapsack absent	critical
Example creation (`pred create --example Knapsack`)	No canonical model example (pre-existing)	info
Solving via brute-force	PASS — correct solutions	—
Reduction (`pred reduce ... --to ILP`)	Works but takes indirect 2-step path (Knapsack→QUBO→ILP) producing 28 vars instead of expected 4	major
Round-trip correctness	PASS — solutions map back correctly	—
Edge cases (empty, single, zero-capacity)	PASS	—
Unit tests (`make test`)	All 2254 pass	—

Critical Finding: Knapsack→ILP reduction not registered in CLI binary

The inventory::submit! registration generated by #[reduction] is collected in the test binary but not in the CLI binary. Evidence:

pred list --rules shows 0 Knapsack→ILP entries
pred path Knapsack ILP returns 2-step path through QUBO instead of direct 1-step
Unit test test_knapsack_to_ilp_path_exists passes (asserts direct path exists) — test binary and CLI binary disagree
The module is properly declared in rules/mod.rs under #[cfg(feature = "ilp-solver")], and the feature IS enabled
Other structurally identical ILP reductions (e.g., binpacking_ilp) register correctly

Root cause hypothesis: inventory crate linker-section registration intermittently fails for certain object files when compiled as a library dependency (vs test binary with direct linking). May be exacerbated by LTO on macOS. This appears to be a systemic issue also affecting 2 other reductions in release builds (MinimumFeedbackVertexSet→ILP, MinimumMultiwayCut→ILP).

Pre-existing findings (not from this PR):

pred create Knapsack with data flags fails (no match arm in create.rs) — minor
Unreachable pattern warning in create.rs:236 — info

Generated by review-pipeline

Resolve conflicts: - references.bib: keep both sides' new entries - examples.json: remove legacy file (deleted on main)

The direct_ilp_example helper was removed on main. Update to use the current rule_example_with_witness API with an explicit SolutionPair.

GiggleLiu added 4 commits March 17, 2026 04:19

Add plan for #639: [Rule] Knapsack to ILP

0cad725

Implement #639: [Rule] Knapsack to ILP

5c2b810

Add extra tests for #639 Knapsack -> ILP

a457a66

chore: remove plan file after implementation

e83ab1f

GiggleLiu requested a review from Copilot March 16, 2026 20:42

Copilot started reviewing on behalf of GiggleLiu March 16, 2026 20:43 View session

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isPANN self-assigned this Mar 20, 2026

isPANN added 2 commits March 20, 2026 14:05

Merge origin/main into issue-639-knapsack-to-ilp

8333507

Resolve conflicts: - references.bib: keep both sides' new entries - examples.json: remove legacy file (deleted on main)

Fix canonical example to use rule_example_with_witness API

91345cf

The direct_ilp_example helper was removed on main. Update to use the current rule_example_with_witness API with an explicit SolutionPair.

isPANN approved these changes Mar 20, 2026

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isPANN mentioned this pull request Mar 20, 2026

[Rule] Knapsack to ILP #639

Closed

isPANN merged commit 418222f into main Mar 20, 2026
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GiggleLiu deleted the issue-639-knapsack-to-ilp branch April 12, 2026 00:53

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Fix #639: [Rule] Knapsack to ILP#688

Fix #639: [Rule] Knapsack to ILP#688
isPANN merged 6 commits intomainfrom
issue-639-knapsack-to-ilp

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