science

Query evaluation

Query evaluation 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 Query evaluation rather than just read about it. In short: In database theory, the query evaluation problem is the problem of determining the answers to a query on a database. Research in database theory aims at determining the computational complexity of answering different kinds of queries over databases, in particular over relational databases.

Key takeaways

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

Reference excerpt

In database theory, the query evaluation problem is the problem of determining the answers to a query on a database. Research in database theory aims at determining the computational complexity of answering different kinds of queries over databases, in particular over relational databases.

Formal definition The query evaluation problem takes two inputs: the query to be answered, and the database on which to answer it. The output of the problem is the set of answers to the query on the database. If the queries are Boolean queries, i.e., queries have a yes or no answer (for example, Boolean conjunctive queries) then the query evaluation problem is a decision problem. The query evaluation problem is usually posed for a specific class of queries and databases. For instance, one example of the query evaluation problem would be the problem of evaluating a conjunctive query on a relational database. The computational complexity of the problem can be measured in different ways, to account for the fact that the two inputs of the problem are different:

The combined complexity of the query evaluation problem is its computational complexity when measured as a function of the two inputs, i.e., the query and the database, as usual in computational complexity. The data complexity is the computational complexity when the query is fixed and when the input is just the database. For instance, we say that query evaluation has polynomial-time data complexity for a class of queries if, for every fixed query Q in that class, given a database D, we can compute the answers to Q on D in polynomial time. Less commonly, we can study the query complexity, which is the computational complexity when the database is fixed and when the input is just the query. This is also called expression complexity.

Query classes The complexity of query evaluation can be studied for several query classes, for instance acyclic queries, conjunctive queries, unions of conjunctive queries, Datalog, regular path queries, etc., up to logical formalisms like first-order logic or monadic second-order logic. For instance, for Boolean conjunctive queries, the complexity of query evaluation is polynomial in data complexity: it even falls in the class AC0. By contrast, the query complexity and combined complexity are NP-complete by a reduction from 3-colorability.

Boolean versus non-Boolean queries The complexity of query evaluation can be studied for queries that return answers, or for Boolean queries (yes/no queries). However, we can often reduce to the case of Boolean queries. More specifically, if the number of answers to the query is always polynomial in the database size, and if we can rewrite the query to a Boolean query for each answer, then we can reduce query evaluation for a non-Boolean query to polynomially many Boolean query evaluation problems.

References

Worked examples

Example 1 — a first encounter with Query evaluation

Start with the simplest possible case. Write down what Query evaluation 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 Query evaluation 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 Query evaluation 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 Query evaluation

In research: Query evaluation 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 Query evaluation 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: Query evaluation is common in secondary-school and first-year university syllabi. It links to neighbouring topics Database theory, so understanding it makes those chapters shorter.
In everyday life: Look for Query evaluation 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.

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How to study Query evaluation in 20 minutes

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

Frequently asked questions

What is Query evaluation in simple terms?

Why does Query evaluation 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 Query evaluation?

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 Query evaluation.