Make MIS → KingsSubgraph reduction deterministic (#1061)

[isPANN]

Summary

Fixes #1061. pred reduce output for MIS<SimpleGraph, One> → MIS<KingsSubgraph, One> now produces byte-identical bundles across repeated invocations on the same input. Three pred reduce runs on a 64-vertex MIS used to vary ~15–20 % in atom/edge count; they now match exactly.

Root cause

Two compounding sources of non-determinism in src/rules/unitdiskmapping/pathdecomposition.rs:

1. Unseeded RNG — greedy_step used rand::rng() (thread-local, OS-seeded) to pick among tied candidates. Compounded by pathwidth's 10 random restarts for >30-vertex inputs.
2. HashSet iteration order — AdjList was Vec<HashSet<usize>>. When vsep_updated_neighbors did for &w in &adj[v] { nbs.push(w); }, per-process HashSet iteration order leaked into layout.neighbors, which then fed the next greedy step. Seeding the RNG alone was not enough (I hit this: same seed, different output — which is how I found this second source).

Fix

• Change AdjList from Vec<HashSet<usize>> to Vec<BTreeSet<usize>> so iteration is deterministic (sorted).
• Thread a SmallRng through greedy_step / greedy_decompose / pathwidth, seeded from new DEFAULT_PATHWIDTH_SEED = 0 so the public API is reproducible by default.
• Add pathwidth_with_seed(.., seed) as an escape hatch for callers that want to sample the layout space. Single SmallRng threads through all 10 restarts so each restart remains diverse (RNG state progresses) while overall output is reproducible given the seed.
• reduce_to() stays a pure function — no env vars, no global state, no trait changes.

Non-goals (tracked separately)

• --seed flag on pred reduce — would require plumbing an optimization hyperparameter through ReduceTo::reduce_to(&self); out of scope for a determinism fix.
• Sampling K seeds and picking minimum-atom mapping — opened as Seeded search for minimum-atom MIS → KingsSubgraph mapping #1062.

Tests

Three new tests (all passing):

• test_pathwidth_greedy_is_deterministic — 64-vertex grid graph, 4 pathwidth calls must yield identical vertex orderings and vsep.
• test_pathwidth_with_seed_varies_output — confirms seed actually threads into tie-breaking (same seed → same output; at least one seed in 1..=10 → different output).
• test_mis_simple_one_to_kings_one_is_deterministic_on_large_graph — end-to-end regression for the reporter's 64-vertex scenario; 4 reduce_to calls must agree on target num_vertices and num_edges.

Full suite: 4960 library tests + 316 CLI tests pass. cargo clippy and cargo fmt --check clean.

Test plan

• cargo test --lib (4960 pass, 0 fail)
• cargo test -p problemreductions-cli (316 pass, 0 fail)
• cargo clippy --lib --all-features clean
• cargo fmt --check clean
• Manual CLI repro: 3× pred reduce on 64-vertex MIS produce byte-identical diff-empty bundles

🤖 Generated with Claude Code

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 97.92%. Comparing base (b3b18f1) to head (84c67d4).

Additional details and impacted files

@@           Coverage Diff            @@
##             main    #1063    +/-   ##
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  Coverage   97.92%   97.92%            
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  Files         966      966            
  Lines      100043   100153   +110     
========================================
+ Hits        97967    98076   +109     
- Misses       2076     2077     +1     

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