Persistent shared DAG for constraint propagation

[dpsanders]

Summary

• Redesigns the DAG engine so the graph is persistent (built once, reused across all pave iterations) and shared across constraints
• SharedDAG is the central object that accumulates constraints via add_expression!. Variable nodes and common subexpressions are reused across all expressions added to the same DAG.
• Multi-constraint propagation: propagate!(dag, X) contracts all constraints jointly each iteration, so narrowing from one constraint immediately benefits others through shared variable nodes
• DAGContractor(dag, expr, vars) and DAGSeparator(dag, expr, vars, constraint) accept an existing SharedDAG, letting multiple separators share the same graph

Key results

Node sharing: Two expressions x²+y²-1 and x²-y on the same SharedDAG use 10 nodes vs 15 separate (33% fewer — the x² subexpression is shared).

Joint propagation: x²+y²≤1 AND x²-y≤0 on [-10,10]² correctly narrows to [-1,1]×[0,1] in a single propagate! call, because the second constraint forces y≥x²≥0.

Benchmarks (persistent DAG vs code-generation):

Problem	ϵ	Codegen	DAG	Ratio
Unit disk 2D	single call	1.2 μs	6.8 μs	6x
Unit disk 2D	0.1	294 μs	2.5 ms	8x
Unit disk 2D	0.01	2.5 ms	20 ms	8x
Annulus 2D	0.1	1.7 ms	10 ms	6x
3D torus	1.0	12 ms	97 ms	8x

Both approaches produce identical paving results on all test cases.

Usage

# Standalone (creates its own DAG):
S = DAGSeparator(x^2 + y^2 <= 1, [x, y])
inner, boundary = pave(X, S, 0.1)

# Shared DAG (multiple constraints, joint propagation):
dag = SharedDAG([x, y])
S1 = DAGSeparator(dag, x^2 + y^2 - 1, [x, y], interval(-Inf, 0.0))
S2 = DAGSeparator(dag, x^2 - y, [x, y], interval(-Inf, 0.0))
result = propagate!(dag, IntervalBox(interval(-10, 10), 2))

Test plan

• 13 test sets in test/test_dag.jl — SharedDAG construction, CSE node reuse, multi-constraint propagation, shared DAG contractors/separators, paving comparison with original, combined separators, 3D
• All 4 existing test sets in test/runtests.jl still pass
• Benchmarks in benchmark/bench_dag_vs_codegen.jl

🤖 Generated with Claude Code