Branch-and-Bound Algorithms as Polynomial-time Approximation Schemes
Hey there, little explorer! 👋
Imagine you have a big toy box, and you want to find your favorite teddy bear super fast!
Sometimes, we have a special way to look for it, like "Branch-and-Bound." It's like checking every part of the box very carefully until you find the exact bear. It takes a long time, but you always find it!
But what if you don't have all day? This smart paper says that sometimes, this careful way of looking can also be like a "speedy search." It means you might not find the perfect bear right away, but you can find a really good bear much, much faster! And the more time you give it, the closer it gets to being perfect!
So, it's like learning that your super careful search can also be a super speedy search! How cool is that? 🎉
arXiv:2504.15885v3 Announce Type: replace 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
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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
Subjects:
Data Structures and Algorithms (cs.DS); Optimization and Control (math.OC)
Cite as: arXiv:2504.15885 [cs.DS]
(or arXiv:2504.15885v3 [cs.DS] for this version)
https://doi.org/10.48550/arXiv.2504.15885
arXiv-issued DOI via DataCite
Journal reference: Mathematics of Operations Research, 2026 Mathematics of Operations Research Mathematics of Operations Research
Submission history
From: Eleonora Vercesi [view email] [v1] Tue, 22 Apr 2025 13:30:01 UTC (317 KB) [v2] Tue, 16 Sep 2025 08:43:07 UTC (823 KB) [v3] Thu, 2 Apr 2026 15:57:27 UTC (180 KB)
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