Fix #122: Add SteinerTree model

[zazabap]

Summary

• Add SteinerTree problem model — minimum-weight tree connecting terminal vertices in a graph
• Edge-based binary optimization following the TravelingSalesman pattern
• Includes CLI support (dispatch, aliases, create with --terminals flag)
• Dreyfus-Wagner complexity: O(3^|T| · n + 2^|T| · n²)

Fixes #122

[Copilot]

Pull request overview

Adds a detailed implementation plan document for introducing a new SteinerTree problem model (and associated tests/CLI/docs updates) to the codebase.

Changes:

• Adds an implementation plan covering the SteinerTree model structure, validity checking, and trait impls
• Outlines unit tests, CLI integration points, and documentation regeneration steps

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[Copilot]

The PR title/description says the SteinerTree model + CLI support are added, but this PR currently only introduces an implementation plan document. Either update the PR metadata to reflect that this is documentation/planning only, or include the actual code/test/CLI/schema changes described in the plan before merging (so it truly fixes #122).

[Copilot]

In the is_valid_steiner_tree snippet, component_vertices is computed with a very complex expression that appears incorrect and wouldn’t compile as Rust (and the variable is unused). Since this is meant to be a copy/paste starting point, consider removing this line entirely or replacing it with the simpler reachable_involved count described immediately below to avoid confusion.

Suggested change

	// Count vertices in the connected component containing terminals
	let component_vertices: usize = visited.iter().filter(|&&v| v && involved.iter().enumerate().any(|(i, &inv)| inv && i == 0).is_none() || v).count();

[codecov]

Codecov Report

❌ Patch coverage is 98.52941% with 3 lines in your changes missing coverage. Please review.
✅ Project coverage is 96.90%. Comparing base (5fbde0e) to head (67122bb).

Files with missing lines	Patch %	Lines
src/models/graph/steiner_tree.rs	97.27%	3 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #192      +/-   ##
==========================================
+ Coverage   96.88%   96.90%   +0.01%     
==========================================
  Files         200      202       +2     
  Lines       27537    27741     +204     
==========================================
+ Hits        26680    26882     +202     
- Misses        857      859       +2     

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[zazabap]

Implementation Summary

Changes

• src/models/graph/steiner_tree.rs — New model: SteinerTree<G, W> with edge-based binary variables, validity checker (connected + acyclic + terminals covered), Problem/OptimizationProblem impls, declare_variants! with Dreyfus-Wagner complexity
• src/unit_tests/models/graph/steiner_tree.rs — 12 unit tests covering creation, evaluation (valid/invalid/empty), direction, size getters, is_weighted, brute-force, MST special case, serialization
• src/models/graph/mod.rs, src/lib.rs — Registration and prelude export
• problemreductions-cli/src/dispatch.rs — load_problem + serialize_any_problem match arms
• problemreductions-cli/src/problem_name.rs — ST/steiner aliases
• problemreductions-cli/src/commands/create.rs — parse_terminals, create handler, example, random generation
• problemreductions-cli/src/cli.rs — --terminals flag
• docs/paper/reductions.typ — problem-def entry with background, Dreyfus-Wagner/Byrka citations, example figure
• docs/paper/references.bib — Added dreyfuswagner1971, byrka2013
• docs/src/reductions/problem_schemas.json, reduction_graph.json — Regenerated

Deviations from Plan

• None significant. The validity checker pseudocode in the plan had rough spots (dead code, confusing comments); the implementation cleans it up to a straightforward BFS + tree property check.

Open Questions

• None