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. Cependant, 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.

Cet article explore les excursions dans le temps et leurs implications.

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