Is bin packing 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. .

Which bin packing algorithm is best?

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.

How do you solve bin packing problems?

Use a new bin only if it does not.


  1. Loading of containers like trucks.
  2. Placing data on multiple disks.
  3. Job scheduling.
  4. Packing advertisements in fixed length radio/TV station breaks.
  5. Storing a large collection of music onto tapes/CD’s, etc.

What is online bin packing problem?

Bin packing is a classic optimization problem with a wide range of applications from load balancing in networks to supply chain management. In this work we study the online variant of the problem, in which a sequence of items of various sizes must be placed into a minimum number of bins of uniform capacity.

Is bin packing a decision problem?

The BIN PACKING decision problem asks the question whether – given a set of objects of distinct sizes, and a set of bins with specific capacity – there is a distribution of items to bins such that no item is left unpacked nor the capacity of any bin is exceeded.

What is bin packing in Kubernetes?

Bin packing – how well you pack applications onto your Kubernetes nodes. The better you pack apps onto nodes, the more you save. App right-sizing – the ability to set appropriate resources requests and workload autoscale configurations for the applications deployed in the cluster.

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.

What is the first fit bin packing algorithm?

First-fit (FF) is an online algorithm for bin packing. Its input is a list of items of different sizes. Its output is a packing – a partition of the items into bins of fixed capacity, such that the sum of sizes of items in each bin is at most the capacity.

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]. All the bins are identical with width W and height H, and each item i ∈ I has a specific width wi and height hi.

How do you spread pods across nodes?

In order to distribute pods evenly across all cluster worker nodes in an absolute even manner, we can use the well-known node label called as a topology domain, which ensures each worker node is in its own topology domain.

How do you schedule pods in Kubernetes?

You can use any of the following methods to choose where Kubernetes schedules specific Pods:

  1. nodeSelector field matching against node labels.
  2. Affinity and anti-affinity.
  3. nodeName field.
  4. Pod topology spread constraints.

How does bin packing work?

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 is packing problems in math?

Packing problems are a class of optimization problems in mathematics that involve attempting to pack objects together into containers. The goal is to either pack a single container as densely as possible or pack all objects using as few containers as possible.

How do you distribute pods evenly?

What is difference between Daemonset and deployment?

A Daemonset will not run more than one replica per node. Another advantage of using a Daemonset is that, if you add a node to the cluster, then the Daemonset will automatically spawn a pod on that node, which a deployment will not do.

Can a pod run on multiple nodes?

The key thing about pods is that when a pod does contain multiple containers, all of them are always run on a single worker node—it never spans multiple worker nodes, as shown in figure 3.1.

How many pods can run on a node?

Overview. By default, GKE allows up to 110 Pods per node on Standard clusters, however Standard clusters can be configured to allow up to 256 Pods per node. Autopilot clusters have a maximum of 32 Pods per node.

What is a packing pattern?

1. Solves the pattern selection problem for constructing pattern database search heuristics. One bin represents a container for the abstract state space and approximates the memory usage for pattern database construction. Multiple bins apply for disjoint pattern database construction.

How do you do the container packing in math?

Container Packing || N5 Applications of Maths Units – YouTube

Does Kubernetes rebalance pods?

5/ In other words, Kubernetes does not rebalance your pods automatically.

What is POD topology?

You can use topology spread constraints to control how Pods are spread across your cluster among failure-domains such as regions, zones, nodes, and other user-defined topology domains. This can help to achieve high availability as well as efficient resource utilization.

What is difference between StatefulSet and DaemonSet?

Statefulsets is used for Stateful applications, each replica of the pod will have its own state, and will be using its own Volume. DaemonSet is a controller similar to ReplicaSet that ensures that the pod runs on all the nodes of the cluster.

Can you run two pods on each node using DaemonSet?

DaemonSet can create multiple pods per node during failover, does not give at-most-one semantics #54096. kind/bug. lifecycle/rotten. sig/apps.

How many containers a pod can have?

No more than 5000 nodes. No more than 150000 total pods. No more than 300000 total containers.

Can we create pod without container?

Workloads use metadata resources, which are the objects used to configure the behavior of other resources within the cluster. Workloads will eventually run a container, but to run a container, you will need to run a Pod. It is possible to create a Pod as a standalone object.