## What is the best bin packing algorithm?

The best existing algorithm for optimal bin packing is due to Martello and Toth (Martello & Toth 1990a; 1990b). We present a new algorithm for optimal bin packing, which we call bin completion, that explores a different problem space, and appears to be asymptotically faster than the Martello and Toth algorithm.

## What is 2D bin packing?

The two-dimensional bin packing problem (2D-BPP) consists of packing without overlap, a set I of two-dimensional rectangular items into the minimum number of two-dimensional rectangular bins [1–3]. Example for 2D-BPP. Optimal configuration for an instance from [4] with two bins and more than 50 items.

Is bin packing NP hard?

Hardness of bin packing The bin packing problem is strongly NP-complete. This can be proven by a reduction from the partition problem: given an instance of Partition where the sum of all input numbers is 2 T, construct an instance of bin-packing in which the bin size is T.

What is bin packing used for?

Bin packing involves packing a set of items of different sizes in containers of various sizes. The size of the container shouldn’t be bigger than the size of the objects. The goal is to pack as many items as possible in the least number of containers possible.

### 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”.

### What is the hardest NP problem?

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.

Is there a packing algorithm for 2D bin packing?

A packing algorithm for 2D bin packing. Largely based on code and a blog post by Jake Gordon. This library packs objects that have a width and a height into as small of a square as possible, using a binary tree bin packing algorithm. After packing, each object is given an (x, y) coordinate of where it would be optimally packed.

How to solve an offline bin packing problem?

This online calculator tries to solve an offline two-dimensional (2D) bin packing problem using Maximal Rectangles heuristic algorithm

#### 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.

#### Which is the second phase of the packing algorithm?

The second phase adopts the First-Fit Decreasing (FFD) algorithm, which packs an item to the first bin that it fits or start a new bin otherwise. Time complexity: O (n·log n). The approximation ratio of HFF is 17/8 [4] . The bound is not proved to be tight: the best lower bound of HFF known is 91/45. NFDH is adopted in the first phase.