science

Quadratic bottleneck assignment problem

Quadratic bottleneck assignment problem is a science topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Quadratic bottleneck assignment problem rather than just read about it. In short: In mathematics, the quadratic bottleneck assignment problem (QBAP) is one of the fundamental combinatorial optimization problems in the branch of optimization or operations research, from the category of the facilities location problems. It is related to the quadratic assignment problem in the same way as the linear bottleneck assignment problem is related to the linear assignment problem, the "sum" is replaced with…

Key takeaways

Quadratic bottleneck assignment problem belongs to science; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Quadratic bottleneck assignment problem to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Quadratic bottleneck assignment problem from memory before moving on to harder problems.

Reference excerpt

In mathematics, the quadratic bottleneck assignment problem (QBAP) is one of the fundamental combinatorial optimization problems in the branch of optimization or operations research, from the category of the facilities location problems. It is related to the quadratic assignment problem in the same way as the linear bottleneck assignment problem is related to the linear assignment problem, the "sum" is replaced with "max" in the objective function. The problem models the following real-life problem:

There are a set of n facilities and a set of n locations. For each pair of locations, a distance is specified and for each pair of facilities a weight or flow is specified (e.g., the amount of supplies transported between the two facilities). The problem is to assign all facilities to different locations with the goal of minimizing the maximum of the distances multiplied by the corresponding flows.

Computational complexity The problem is NP-hard, as it can be used to formulate the Hamiltonian cycle problem by using flows in the pattern of a cycle and distances that are short for graph edges and long for non-edges.

Special cases Bottleneck traveling salesman problem Graph bandwidth problem

References

Worked examples

Example 1 — a first encounter with Quadratic bottleneck assignment problem

Start with the simplest possible case. Write down what Quadratic bottleneck assignment problem claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In science, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Quadratic bottleneck assignment problem before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Quadratic bottleneck assignment problem ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Quadratic bottleneck assignment problem

In research: Quadratic bottleneck assignment problem appears in science research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Quadratic bottleneck assignment problem in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Quadratic bottleneck assignment problem is common in secondary-school and first-year university syllabi. It links to neighbouring topics Combinatorial optimization, NP-hard problems, so understanding it makes those chapters shorter.
In everyday life: Look for Quadratic bottleneck assignment problem outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

Affiliate

Preply — study more efficiently by working with a personal tutor. 50% off.

How to study Quadratic bottleneck assignment problem in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Quadratic bottleneck assignment problem means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Quadratic bottleneck assignment problem out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Quadratic bottleneck assignment problem in simple terms?

Why does Quadratic bottleneck assignment problem matter?

Because it connects several science ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Quadratic bottleneck assignment problem?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Quadratic bottleneck assignment problem.