Branch-and-Bound-Algorithmen (B&B) und Polynomzeit-Approximationsschemata
(PTAS) sind zwei scheinbar weit entfernte Bereiche der kombinatorischen Optimierung. We intend
Zu (teilweise) bridge the gap between them while expanding the boundary of
theoretical knowledge on the B&B-Rahmen. Branch-and-Bound-Algorithmen
typically guarantee that an optimal solution is eventually found. Jedoch, Wir
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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