arXiv:2610.35948 · v2

Native Rectangular Linear Assignment with Implicit Rejection: A Jonker-Volgenant Solver without Square Expansion

首次提交 2026-10-24 17:42

版本更新 2026-11-08 21:57

雷达观测 2026-11-10 12:16

摘要

Rectangular assignment with a uniform unmatched penalty is often implemented by expanding the cost matrix. We integrate established rectangular Jonker-Volgenant principles and implicit rejection with float64 working arithmetic and reusable workspaces in Rust (JVRUST), hybrid Rust/C++ (JVHYBRID) and C++ (JVCPP). A campaign evaluates laprust/lapcpp 1.2.0 and LAPX 0.13.0 in four Windows/Linux and Python environments. Each environment contains 302 cases: 3,286 complete-call timing conditions with five inputs and three rounds, plus 91 memory conditions with five fresh-process trials. Against the matching compact SciPy reference, all three native implementations exceed a 3% advantage on all 102 required cases; JVRUST and JVCPP do so on 163-165 and 163-166 of 166 optional cases, respectively. Controlled comparisons qualify these gains by representation, initialization, sparsity, batching and orientation. Assignment-replay gains attenuate in tracker updates, and equal replay objectives do not imply identical tracking outputs. A separate 67-case Windows LSAPE study examines related transformations within Hungarian code. The contribution is software integration and reproducible performance characterization. Adverse results are retained; no algorithmic priority, statistical significance or universal solver ranking is claimed. The initialization policy was developed using related workload families, so the campaign is not a held-out test of heuristic optimality.

作者备注：32 pages, 14 figures. v2: updated benchmark methodology and results, redesigned figures, and updated author list