Is bin packing problem NP-hard?

Hardness of bin packing The bin packing problem is strongly NP-complete. This can be proven by reducing the strongly NP-complete 3-partition problem to bin packing.

What does NP-hard stand for?

non-deterministic polynomial-time hardness
In computational complexity theory, NP-hardness (non-deterministic polynomial-time hardness) is the defining property of a class of problems that are informally “at least as hard as the hardest problems in NP”. A simple example of an NP-hard problem is the subset sum problem.

How is the bin packing problem a combinatorial NP hard problem?

In the bin packing problem, items of different volumes must be packed into a finite number of bins or containers each of volume V in a way that minimizes the number of bins used. In computational complexity theory, it is a combinatorial NP-hard problem.

What are the applications of the bin packing problem?

Background. The bin packing problem consists of packing items of varying sizes into a finite number of bins of fixed capacity. The objective is to minimize the number of bins used to pack all the items. Applications of the bin packing problem are wide ranging and include loading trucks, scheduling tasks, manufacturing items from resources,

Which is the proof of the bin packing theorem?

Algorithms K.V.Iyer Theorem: The bin packing problem is NP−hard. The proof follows from a reduction of the subset-sum problem to bin packing. The First-Fit Decreasing Heuristic (FFD) • FFD is the traditional name – strictly, it is first-fit nonincreasing. • An early known approximation algorithm. • Works on greedy strategy.

Is the bin packing problem a polynomial time problem?

The bin packing problem is strongly NP-complete. This can be proven by reducing the strongly NP-complete 3-partition problem to bin packing. On the other hand, it is solvable in pseudo-polynomial time for each fixed K ≥ 2 {\\displaystyle K\\geq 2} and solvable in polynomial time for each fixed B {\\displaystyle B} . [5]