The Strength of Root Cuts in an Extended Abstract Branch-and-Cut Model

@misc{han2026strength,
  title = {{The Strength of Root Cuts in an Extended Abstract Branch-and-Cut Model}},
  author = {Boyang Han and Aleksandr M. Kazachkov},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.31774},
  eprint = {2610.31774},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.31774},
}

TY  - UNPB
TI  - The Strength of Root Cuts in an Extended Abstract Branch-and-Cut Model
AU  - Boyang Han
AU  - Aleksandr M. Kazachkov
PY  - 2026
DA  - 2026/10/22
PB  - arXiv
DO  - 10.48550/arxiv.2610.31774
UR  - https://arxiv.org/abs/2610.31774
AB  - The branch-and-cut paradigm has led to effective solvers for a wide range of mathematical optimization problems. Despite significant theoretical work on pure branching and pure cutting, less is known about their interaction. We study an extended abstract branch-and-cut model to investigate tradeoffs between branching and cutting, including the time to generate cuts. We prove that, under symmetric branching, some minimal-time tree has all cuts at the root, before the first branching node, and that there is an asymmetric setting where some minimal-time tree has no internal cuts, i.e., cuts both preceded and followed by branching. For other settings, although a root-cut tree may be suboptimal and differ substantially in structure from a minimal-time tree, it nevertheless provides a reliable approximation whose tree time does not deviate arbitrarily from the optimum. For constant cut strength and bounded time functions, we show that the best root-cut tree is asymptotically optimal as the target bound grows. In addition, under a single-cut-per-path restriction, we characterize when some minimal-time tree has an internal cut. Lastly, simulations indicate that the best root-cut tree is much closer to a minimal-time tree than our worst-case approximation guarantee suggests.
ER  -