Show HN: Malloc – phy solver for constrained balanced partitioning problems (codeberg.org)

malloc (MultiplicativeConstraint) is a new partitioning engine that uses heat-kernel spectral methods and a multiplicative encoding (so-called “prime necklace” graphs) to solve constrained balanced partitioning problems dramatically faster than conventional solvers. The authors don’t claim to solve P=NP — instead they target a high-value, structured subset of NP-hard partitioning/clustering tasks (resource allocation, scheduling, EDA, HPC payloads, etc.) and report 60–70× speedups on typical instances. Core empirical wins include solving a 100K-node sparse instance in ~84s with a 23MB footprint (vs ~80GB dense), and a measured spectral-to-objective correlation ρ ≈ 0.996 that justifies substituting hard objectives with spectrally smooth proxies. Technically, malloc combines stochastic heat-trace (Hutchinson) estimates of spectral action Tr(f(D)) implemented with sparse Laplacian matvecs (cost O(s·m·nnz) per eval), multiplicative fairness/entropy penalties on segment aggregates (O(n+nnz)), and annealed optimization with neural surrogates that learn log-prime assignments (training O(S·s·m·nnz), fast inference). Simulated annealing runtime scales as O(R·I·(s·m·nnz)). Benchmarks on an M1 Pro show sub-10s for ~50–60 item problems and robust behavior under adversarial stress (83% constraint satisfaction, graceful degradation when contradictions exist). For the AI/ML community this offers a differentiable, auditable, scalable optimizer for constrained partitioning problems—enabling large-scale scheduling, model/cluster allocation and differentiable surrogate integration—while remaining explicit about its structural scope and limitations.