Maximum agreement subtree problem

Key takeaways

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

Reference excerpt

The maximum agreement subtree problem is any of several closely related problems in graph theory and computer science. In all of these problems one is given a collection of trees T 1 , … , T m {\displaystyle T_{1},\ldots ,T_{m}} each containing n {\displaystyle n} leaves. The leaves of these trees are given labels from some set L {\displaystyle L} with | L | = n {\displaystyle |L|=n} so that no pair of leaves in the same tree sharing the same label, within the same tree the labelling for each leaf is distinct. In this problem one would like to find the largest subset L ′ ⊂ L {\displaystyle L'\subset L} such that the minimal spanning subtrees containing the leaves in L ′ {\displaystyle L'} , of T 1 ∣ S , … , T m ∣ S {\displaystyle T_{1}\mid S,\ldots ,T_{m}\mid S} are the "same" while preserving the labelling.

Formulations

Maximum homeomorphic agreement subtree Source: This version requires that the subtrees T 1 ∣ S , … , T m ∣ S {\displaystyle T_{1}\mid S,\ldots ,T_{m}\mid S} are homeomorphic to one another.

Rooted maximum homeomorphic agreement subtree This version is the same as the maximum homeomorphic agreement subtree, but we further assume that T 1 , … , T m {\displaystyle T_{1},\ldots ,T_{m}} are rooted and that the subtrees T 1 ∣ S , … , T m ∣ S {\displaystyle T_{1}\mid S,\ldots ,T_{m}\mid S} contain the root node. This version of the maximum agreement subtree problem is used for the study of phylogenetic trees. Because of its close ties with phylogeny this formulation is often what is mean when one refers to the "maximum agreement subtree" problem.

Other variants There exits other formulations for example the (rooted) maximum isomorphic agreement subtree where we require the subtrees to be isomorphic to one another.

Worked examples

Example 1 — a first encounter with Maximum agreement subtree problem

Start with the simplest possible case. Write down what Maximum agreement subtree problem claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In computer 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 Maximum agreement subtree 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 Maximum agreement subtree 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 Maximum agreement subtree problem

In research: Maximum agreement subtree problem appears in computer 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 Maximum agreement subtree 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: Maximum agreement subtree problem is common in secondary-school and first-year university syllabi. It links to neighbouring topics Computational problems in graph theory, so understanding it makes those chapters shorter.
In everyday life: Look for Maximum agreement subtree 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.

How to study Maximum agreement subtree problem in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Maximum agreement subtree 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 Maximum agreement subtree problem out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Maximum agreement subtree problem in simple terms?

The maximum agreement subtree problem is any of several closely related problems in graph theory and computer science. In all of these problems one is given a collection of trees T 1 , … , T m {\displaystyle T_{1},\ldots ,T_{m}} each containing n {\displaystyle n} leaves.

Why does Maximum agreement subtree problem matter?

Because it connects several computer 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 Maximum agreement subtree 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 Maximum agreement subtree problem.