Branch-and-Bound Algorithms as Polynomial-time Approximation Schemes
Data Structures and Algorithms
2026-04-03 v3 Optimization and Control
Abstract
Branch-and-bound algorithms (B&B) and polynomial-time approximation schemes (PTAS) are two seemingly distant areas of combinatorial optimization. We intend to (partially) bridge the gap between them while expanding the boundary of theoretical knowledge on the B\&B framework. Branch-and-bound algorithms typically guarantee that an optimal solution is eventually found. However, we show that the standard implementation of branch-and-bound for certain knapsack and scheduling problems also exhibits PTAS-like behavior, yielding increasingly better solutions within polynomial time. Our findings are supported by computational experiments and comparisons with benchmark methods. This paper is an extended version of a paper accepted at ICALP 2025
Cite
@article{arxiv.2504.15885,
title = {Branch-and-Bound Algorithms as Polynomial-time Approximation Schemes},
author = {Koppány István Encz and Monaldo Mastrolilli and Eleonora Vercesi},
journal= {arXiv preprint arXiv:2504.15885},
year = {2026}
}