## 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.

### 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.

#### Why is the full bin packing algorithm optimal?

The full bin packing algorithm is more likely to produce an optimal solution – using the least possible number of bins – than the first fit decreasing and first fit algorithms. It works by matching object so as to fill as many bins as possible.

What is 3D bin packing problem?

The three-dimensional multiple bin packing problem (3D-MBPP) consists of packing a set of items into a number of bins with different dimensions so as to optimize a given objective function, e.g., minimize the number of bins used to pack the items.

What is meant by NP hard?

A problem is NP-hard if an algorithm for solving it can be translated into one for solving any NP- problem (nondeterministic polynomial time) problem. NP-hard therefore means “at least as hard as any NP-problem,” although it might, in fact, be harder.

## What is automatic bin packing?

Automatic bin packing: You provide Kubernetes with a cluster of nodes that it can use to run containerized tasks. You tell Kubernetes how much CPU and memory (RAM) each container needs. Kubernetes can fit containers onto your nodes to make the best use of your resources.

### Is halting problem NP-complete?

– If we had a polynomial time algorithm for the halting problem, then we could solve the satisfiability problem in polynomial time using A and X as input to the algorithm for the halting problem . – Hence the halting problem is an NP-hard problem which is not in NP. – So it is not NP-complete.

#### Are NP-hard problems NP-complete?

A Problem X is NP-Hard if there is an NP-Complete problem Y, such that Y is reducible to X in polynomial time. NP-Hard problems are as hard as NP-Complete problems….Difference between NP-Hard and NP-Complete:

NP-hard NP-Complete
To solve this problem, it do not have to be in NP . To solve this problem, it must be both NP and NP-hard problems.

What is 2D bin packing problem?

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  with two bins and more than 50 items.

What is P in algorithm?

From Wikipedia, the free encyclopedia. In computational complexity theory, P, also known as PTIME or DTIME(n), is a fundamental complexity class. It contains all decision problems that can be solved by a deterministic Turing machine using a polynomial amount of computation time, or polynomial time.

## What makes NP-hard difficult?

A problem is NP-hard if an algorithm for solving it can be translated into one for solving any NP-problem (nondeterministic polynomial time) problem. NP-hard therefore means “at least as hard as any NP-problem,” although it might, in fact, be harder.

### Which is an example of a heuristic for the bin packing problem?

In addition, many heuristics have been developed: for example, the first fit algorithm provides a fast but often non-optimal solution, involving placing each item into the first bin in which it will fit. It requires Θ(n log n) time, where n is the number of items to be packed.

#### Are there any approximations for the bin packing problem?

Approximation algorithms for bin packing can be classified into two categories: Online heuristics, that consider the items in a given order and place them one by one inside the bins. These heuristics are also applicable to the online version of this problem.

Which is a variant of bin packing of interest?

Another variant of bin packing of interest in practice is the so-called online bin packing. Here the items of different volume are supposed to arrive sequentially and the decision maker has to decide whether to select and pack the currently observed item, or else to let it pass.

When do items share space when packed into a bin?

A variant of bin packing that occurs in practice is when items can share space when packed into a bin. Specifically, a set of items could occupy less space when packed together than the sum of their individual sizes. This variant is known as VM packing since when virtual machines (VMs) are packed in a server,…