computer science

Priority search tree

Priority search tree is a computer 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 Priority search tree rather than just read about it. In short: In computer science, a priority search tree is a tree data structure for storing points in two dimensions. It was originally introduced by Edward M.

Key takeaways

Priority search tree 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 Priority search tree to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Priority search tree from memory before moving on to harder problems.

Reference excerpt

In computer science, a priority search tree is a tree data structure for storing points in two dimensions. It was originally introduced by Edward M. McCreight. It is effectively an extension of the priority queue with the purpose of improving the search time from O(n) to O(s + log n) time, where n is the number of points in the tree and s is the number of points returned by the search.

Description The priority search tree is used to store a set of 2-dimensional points ordered by priority and by a key value. This is accomplished by creating a hybrid of a priority queue and a binary search tree. The result is a tree where each node represents a point in the original dataset. The point contained by the node is the one with the lowest priority. In addition, each node also contains a key value used to divide the remaining points (usually the median of the keys, excluding the point of the node) into a left and right subtree. The points are divided by comparing their key values to the node key, delegating the ones with lower keys to the left subtree, and the ones strictly greater to the right subtree.

Operations

Construction The construction of the tree requires O(n log n) time and O(n) space. A construction algorithm is proposed below:

However, if the points are sorted by their key values then the tree can be constructed in linear time. This can easily be done by constructing a balanced binary tree over the key values (as leaves) in linear time. Each internal node stores a pointer to the lowest priority node and count of number of items in the subtree rooted at that node. Thus, the node with minimum priority can be identified in constant time. The median of remaining points and the item with next smallest priority can be identified in O(log n) time. Thus, the recurrence relation is T(n)=2T(n/2)+O(log n)=O(n).

Grounded range search The priority search tree can be efficiently queried for a key in a closed interval and for a maximum priority value. That is, one can specify an interval [min_key, max_key] and another interval [-∞, max_priority] and return the points contained within it. This is illustrated in the following pseudo code:

Worked examples

Example 1 — a first encounter with Priority search tree

Start with the simplest possible case. Write down what Priority search tree 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 Priority search tree 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 Priority search tree 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 Priority search tree

In research: Priority search tree 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 Priority search tree 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: Priority search tree is common in secondary-school and first-year university syllabi. It links to neighbouring topics Geometric data structures, Trees (data structures), so understanding it makes those chapters shorter.
In everyday life: Look for Priority search tree 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 Priority search tree in 20 minutes

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

Frequently asked questions

What is Priority search tree in simple terms?

In computer science, a priority search tree is a tree data structure for storing points in two dimensions. It was originally introduced by Edward M.

Why does Priority search tree 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 Priority search tree?

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 Priority search tree.