Fix #116: Add Knapsack to QUBO reduction

[zazabap]

Summary

• Adds implementation plan for Knapsack → QUBO reduction rule
• Encodes capacity constraint as equality using binary slack variables (⌊log₂C⌋+1 bits)
• QUBO objective: −∑v_i·x_i + P·(constraint)² with P > ∑v_i

Closes #116

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 96.91%. Comparing base (a88812b) to head (eacb62b).
⚠️ Report is 2 commits behind head on main.

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #172      +/-   ##
==========================================
+ Coverage   96.88%   96.91%   +0.02%     
==========================================
  Files         200      204       +4     
  Lines       27537    27768     +231     
==========================================
+ Hits        26680    26911     +231     
  Misses        857      857              

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[Copilot]

Pull request overview

Adds a new Knapsack problem model and wires in a Knapsack → QUBO reduction (via binary slack variables + quadratic penalty), including tests, CLI support, examples, and documentation/exports.

Changes:

• Introduces Knapsack as a first-class problem model (schema-registered, exported in prelude, unit-tested).
• Implements and registers the Knapsack → QUBO reduction rule with closed-loop brute-force tests and an example exporter.
• Updates CLI alias/dispatch plus regenerates reduction graph + schemas and adds paper documentation for Knapsack and the new rule.

Reviewed changes

Copilot reviewed 19 out of 19 changed files in this pull request and generated 2 comments.

Show a summary per file

File	Description
tests/suites/examples.rs	Registers the new reduction_knapsack_to_qubo example in the examples test suite.
src/unit_tests/rules/knapsack_qubo.rs	Adds closed-loop tests validating the reduction against brute-force optimal solutions.
src/unit_tests/models/misc/knapsack.rs	Adds unit tests for Knapsack model behavior and serialization.
src/rules/mod.rs	Registers the new knapsack_qubo rule module.
src/rules/knapsack_qubo.rs	Implements Knapsack → QUBO reduction and solution extraction.
src/models/mod.rs	Re-exports Knapsack from models.
src/models/misc/mod.rs	Adds knapsack module and re-export in misc category.
src/models/misc/knapsack.rs	Implements the Knapsack model, schema registration, evaluation logic, and variant declaration.
src/lib.rs	Exposes Knapsack via the crate prelude.
problemreductions-cli/src/problem_name.rs	Adds KS / knapsack alias resolution.
problemreductions-cli/src/dispatch.rs	Adds load/serialize dispatch for Knapsack.
problemreductions-cli/src/commands/graph.rs	Removes stray whitespace (no functional change).
examples/reduction_knapsack_to_qubo.rs	Adds an example program exporting the reduction instance + result JSON.
docs/src/reductions/reduction_graph.json	Regenerates reduction graph to include Knapsack and Knapsack → QUBO.
docs/src/reductions/problem_schemas.json	Regenerates problem schemas to include Knapsack.
docs/plans/2026-03-04-knapsack-to-qubo.md	Adds implementation plan document for the reduction.
docs/plans/2026-03-04-knapsack-model.md	Adds implementation plan document for the model.
docs/paper/references.bib	Adds Knapsack-related bibliography entries.
docs/paper/reductions.typ	Adds Knapsack problem definition and the Knapsack → QUBO reduction write-up + example.

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[zazabap]

Mistakes found.

[GiggleLiu]

I have merged #171 , please rebased on the main branch. We'd better not simultaneouly work on models and rules to avoid diverged history.