Priority Queues

Designing and analyzing priority queues.

Priority queue interface
1. PriorityNode
2. Reference implementation
Design and implement
Analyze and compare
1. Affordance analysis
2. Asymptotic analysis

Online social media platforms facilitate the development of social relationships between users by allowing users to create and share content with each other. Most social media platforms rely on algorithms to personalize the content feed presented to each user. This user-generated content requires moderation, or methods for managing content shared between users on the platform.

In this project, we will compare 4 implementations of priority queues to simulate a content moderation queue that might be used in a social media platform where content is generated continuously. By the end of this project, students will be able to:

Design and implement multiple data structures to solve complex problems.
Analyze and compare implementation runtimes and interface affordances.

In the next project, we’ll also use your priority queues as a building block for shortest paths.

What am I submitting at the end of this project?

Satisfactory completion of the project requires a video-recorded team presentation that addresses all the green callouts meeting the following requirements:

Each team member needs to present part of the presentation in order to receive credit for the assignment.
Your presentation should not be much longer than 7 minutes and should include your voiceover. (Your video is appreciated but not necessary.)
Your presentation should include some kind of visually-organizing structure, such as slides or a document.
After submitting to Canvas, add a submission comment linking to your slides or document.

Priority queue interface

The MinPQ interface represents a priority queue that affords access to minimum-priority elements. Priority values are extrinsic to each element: rather than relying on a compareTo method, priority values are specified as arguments to the add and changePriority methods.

void add(E element, double priority): Adds an element with the given priority value if the element is not already in this priority queue.
boolean contains(E element): Returns true if the given element is in this priority queue.
E peekMin(): Returns the element with the minimum priority value.
E removeMin(): Returns and removes an element with the minimum priority value.
void changePriority(E element, double priority): Updates the given element’s associated priority value.
int size(): Returns the number of elements in this priority queue.

The interface also defines two default methods that rely on implementations of the above methods.

void addOrChangePriority(E element, double priority)

Adds an element with the given priority value if it is not already present. Otherwise, updates the priority value of the existing element.

if (!contains(element)) {
    add(element, priority);
} else {
    changePriority(element, priority);
}

boolean isEmpty()

Returns true if this priority queue contains no elements. Returns whether size() == 0.

A MinPQ cannot contain duplicate elements. However, different elements can have the same priority value. peekMin and removeMin may return any element with the minimum priority value.

Here’s a small example showing how to use the MinPQ interface with the DoubleMapMinPQ class included in the project. Try it out for yourself by creating a new class in IntelliJ with the following code in the main method.

MinPQ<String> pq = new DoubleMapMinPQ<>();
pq.add("1", 1.0);
pq.add("2", 2.0);
pq.add("3", 3.0);
pq.add("4", 4.0);
pq.add("5", 5.0);
pq.add("6", 6.0);

// Call methods to evaluate behavior.
pq.changePriority("3", 0.0);
pq.changePriority("1", 7.0);
while (!pq.isEmpty()) {
    System.out.println(pq.removeMin());
}

Why not just implement Java's PriorityQueue interface?

The java.util standard library includes a binary heap PriorityQueue class. Here are three reasons why we can’t implement Java’s PriorityQueue class in this project.

PriorityQueue is a class: We can’t implement the PriorityQueue class because it’s a class, not an interface. Although the Java developers designed Set, Map, and List as interfaces, priority queues are so commonly associated with binary heaps that the Java developers broke the pattern and defined PriorityQueue as a class.
PriorityQueue relies on compareTo: By default, PriorityQueue uses elements’ compareTo method to define the priority of an element. For example, the priority of the string “A” is less than “B” because “A” precedes “B” in the alphabet. This makes PriorityQueue great for sorting objects, but not great for applications like shortest paths.
PriorityQueue disaffords changing priority value: The fact that PriorityQueue uses elements’ compareTo methods reveals a hidden disaffordance. To change the priority of an object in PriorityQueue, we need to remove the element from the priority queue and then re-insert it. This workaround is not only inconvenient, but also inefficient and prone to bugs.

PriorityNode

Java collections typically only specify a single data type as in ArrayList<String>. But a MinPQ needs to keep track of each element as well as its associated priority value. We could do this by creating two lists: an ArrayList<T> for elements and an ArrayList<Double> for each element’s priority value. However, this approach requires us to ensure the state of both lists are always the same, which introduces additional complexity that makes the code harder to maintain and more brittle or susceptible to future bugs.

The PriorityNode class includes two fields representing an element together with its priority value so that it can be used in a Java collection.

List<PriorityNode<String>> elements = new ArrayList<>();
elements.add(new PriorityNode<>("example", 0));

Two PriorityNode objects are considered equal if and only if their elements are equal. Priority values are not checked for equality.

How will this property of PriorityNode equality help you implement MinPQ?

MinPQ does not allow duplicate elements, but does allow duplicate priority values. When using Java collections such as a List, methods like List.contains or List.remove will call the objects’ equals method to check for equality. The following contains call will return true, and the remove call will successfully remove the priority node even though their priority values are different.

elements.contains(new PriorityNode<>("example", 1));
elements.remove(new PriorityNode<>("example", 2));

Reference implementation

The project code includes a working DoubleMapMinPQ. This implementation is called “double map” because it combines the runtime benefits of two maps to solve the problem efficiently. The two maps work together to help achieve sublinear (logarithmic or better) runtime for every operation.

TreeMap: Associates each unique priority value to all the elements with that priority value. Returning a minimum-priority element involves finding the set of minimum-priority elements and picking any element from that set.
HashMap: Associates each element with its priority value in order to speed-up contains and changePriority.

The state of both maps is synchronized across all methods. Any change to one data structure also requires a change to the other data structure.

Design and implement

Design and implement 3 implementations of the MinPQ interface.

All team members must work together and fully understand each implementation. Do not assign each implementation to individual team members. The implementations are described in order of increasing complexity so later implementations will require significantly more work.

UnsortedArrayMinPQ

Elements are added to an ArrayList in any order. Most operations may need to scan over the entire list.

HeapMinPQ

A standard binary heap priority queue that delegates all method calls to java.util.PriorityQueue. In other words, each MinPQ operation is implemented by calling the underlying PriorityQueue. This class contains only one field assigned to an instance of PriorityQueue.

Explain the part of the HeapMinPQ class that you’re most proud of programming.

OptimizedHeapMinPQ

A optimized binary heap priority queue supported by a HashMap that associates each element with its array index to speed-up contains and changePriority. Use the MinPQ class as a reference.

Identify methods in the reference class that are most similar to our interface.
Adapt the code to implement our interface. Make sure all tests pass before optimizing the code.
Optimize the code by adding a HashMap synchronized to the state of the elements in the array.

Explain the part of the OptimizedHeapMinPQ class that you’re most proud of programming.

Analyze and compare

Affordance analysis

Sorting presumes that data can be ordered on a line. Priority queues rely on the same presumption, except that elements are ordered according to their priority values. In the provided Moderator class, messages are entered into an MinPQ with “toxicity” scores provided by the Perspective API, a machine learning algorithm designed to reduce toxicity online.

Toxicity scores represent probabilities between 0 and 1 for the predicted likelihood that a human would perceive the comment as “rude, disrespectful, unreasonable, or otherwise somewhat likely to make the user leave a discussion or give up on sharing their perspective.”

For example, a comment like “You are an idiot” may receive a probability score of 0.8 for attribute TOXICITY, indicating that 8 out of 10 people would perceive that comment as toxic.

Toxicity values are negated before they are added to the MinPQ, so each call to removeMin will remove the message that is most likely to be toxic.

Give an affordance analysis of MinPQ for content moderation when using toxicity scores as the priority value. Identify the affordances of MinPQ. Then, evaluate the affordances by applying the three value-sensitive design principles. Your final arguments may combine ideas from 2 or all 3 principles, so it’s not necessary to present them separately.

Asymptotic analysis

Give a big-theta bound for the worst-case runtime of the removeMin and changePriority methods for each implementation, including DoubleMapMinPQ, with respect to N, the size of the priority queue. Explain the runtime of each implementation in a couple sentences while referencing the code.

For all array-backed data structures, ignore the time it would take to resize the array.

java.util.PriorityQueue is implemented using an array-representation binary heap that

provides O(log(n)) time for the enqueuing and dequeuing methods (offer, poll, remove() and add); linear time for the remove(Object) and contains(Object) methods; and constant time for the retrieval methods (peek, element, and size).

HashSet and HashMap are implemented using resizing separate-chaining hash tables where the number of buckets is always similar to the size. Assume that the hash function evenly distributes elements across the underlying array. The Java implementations include a further optimization.

Tree bucket optimization: When the size of a bucket exceeds 8 elements, the separate chain is automatically converted from a linked list to a red-black tree.

Explain the impact of tree bucket optimization assuming an even distribution of elements across the underlying array. Does the tree bucket optimization help, hurt, or not affect the asymptotic analysis given our assumptions?