Zoom meeting ID: 553-965-838.
Office Hours: Calendar
Welcome to CS166, a course in the design, analysis, and implementation of data structures. We've got an exciting quarter ahead of us - the data structures we'll investigate are some of the most beautiful constructs I've ever come across - and I hope you're able to join us.
CS166 has two prerequisites - CS107 and CS161. From CS107, we'll assume that you're comfortable working from the command-line; designing, testing, and debugging nontrivial programs; manipulating pointers and arrays; using bitwise operators; and reasoning about the memory hierarchy. From CS161, we'll assume you're comfortable designing and analyzing nontrivial algorithms; using O, o, Θ, Ω, and ω notation; solving recurrences; working through standard graph and sequence algorithms; and structuring proofs of correctness.
We'll update this site with more information as we get closer to the start of the quarter. In the meantime, feel free to email me at htiek@cs.stanford.edu if you have any questions about the class!
This syllabus is still under construction and is subject to change as we fine-tune the course. Stay tuned for more information and updates!
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Fusion Trees, Part I
June 2
Memory inside a computer is split apart into individual machine words, with primitive operations like addition, subtraction, and multiplication taking constant time. This means that, if we can pack multiple pieces of data into a single machine word, we can essentially get a limited form of parallel computation. Through a variety of very clever tricks, we can use this to speed up searching and sorting. This first lecture explores word-level parallelism through a data structure for very small integers and a technique for computing most-significant bits in time O(1). It will lay the groundwork we'll use next time when exploring fusion trees. Slides: Readings:
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Fusion Trees, Part II
June 4
The sardine tree we developed in our last lecture gives a fast ordered dictionary data structure for small keys. By harnessing its key insight - B-tree lookups can be sped up by improving rank calculations at each node - and combining it with some insights about integers and Patricia tries, we can build the fusion tree, which works for any integers that fit into a machine word. Slides: |
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Splay Trees
May 26
Red/black trees only move nodes around during insertions or deletions. What happens if we restructure our BSTs every time we perform an operation on them? If you do this properly, the answer is "wonderful things, but we're not sure just how wonderful." Slides: Readings:
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x-Fast and y-Fast Tries
May 28
Balanced BSTs are excellent general-purpose data structures for storing sorted collections of elements. But what happens if we know those elements are integers? By taking advantage of their structure and some nice properties of machine words, we can exponentially improve their performance. Slides: Readings: |
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Cuckoo Hashing
May 19
Most hash tables give expected O(1) lookups. Can we make hash tables with no collisions at all, and if so, can we do it efficiently? Amazingly, the answer is yes. There are many schemes for achieving this, one of which, cuckoo hashing, is surprisingly simple to implement. Slides: Readings:
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Better than Balanced BSTs
May 21
We've been operating under the assumption that a balanced BST that has worst-case O(log n) lookups is, in some sense, an "optimal" binary search tree. In one sense (worst-case efficiency) these trees are optimal. However, there are other perspectives we can take on what "optimal" means, and they counsel toward other choices of tree structures - weight-balanced trees, finger search trees, and Iacono's working set structure. Slides: Readings:
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Count-Min Sketches
May 12
How can Google keep track of frequent search queries without storing all the queries it gets in memory? How can you estimate frequently- occurring tweets without storing every tweet in RAM? As long as you're willing to trade off accuracy for space, you get get excellent approximations. Slides: Readings:
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Count Sketches and Bloom Filters
May 14
We've now seen how to build an estimator: make a simple data structure that gives a good chance of success, then run it in parallel. This idea can be extended to build frequency estimators with other properties and to build estimations of boolean quantities. This lecture is all about the techniques necessary to do this. Slides: Readings:
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Binomial Heaps
May 5
Binomial heaps are a simple and flexible priority queue structure that supports efficient melding of priority queues. The intuition behind binomial heaps is particularly elegant, and they'll serve as a building block toward the more complex Fibonacci heap data structure that we'll talk about on Thursday. Slides: Readings:
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Fibonacci Heaps
May 2
Fibonacci heaps are a type of priority queue that efficiently supports decrease-key, an operation used as a subroutine in many graph algorithms (Dijkstra's algorithm, Prim's algorithm, the Stoer-Wagner min cut algorithm, etc.) They're formed by a clever transformation on a lazy binomial heap. Although Fibonacci heaps have a reputation for being ferociously complicated, they're a lot less scary than they might seem! Slides: Readings:
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Balanced Trees, Part II
April 28
Our last lecture concluded with a view of red/black trees as isometries of 2-3-4 trees. How far does this connection go? How can we use it to derive the rules for red/black trees? And now that we've got red/black trees, what else can we do with them? Slides: Readings:
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Amortized Analysis
April 30
In many cases we only care about the total time required to process a set of data. In those cases, we can design data structures that make some operations more expensive in order to lower the total cost of all aggregate operations. How do you analyze these structures? Slides: Readings:
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Constructing Suffix Arrays
April 21
Suffix trees and suffix arrays are amazing structures, but they'd be much less useful if it weren't possible to construct them quickly. Fortunately, there are some great techniques for building suffix arrays and suffix trees. By using the fact that suffixes overlap and simulating what a multiway merge algorithm would do in certain circumstances, we can rapidly build these beautiful structures. Slides: Readings:
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Balanced Trees, Part I
April 23
Balanced search trees are among the most versatile and flexible data structures. They're used extensively in theory and in practice. What sorts of balanced trees exist? How would you design them? And what can you do with them? Slides Handouts: Readings:
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Tries and Suffix Trees
April 14
To kick off our discussion of string data structures, we'll be exploring tries, Patricia tries, and, most importantly, suffix trees. These data structures provide fast solutions to a number of algorithmic problems and are much more versatile than they might initially seem. What makes them so useful? What properties of strings do they capture? And what intuitions can we build from them? Slides: Handouts: |
Suffix Arrays
April 16
What makes suffix trees so useful as a data structure? Surprisingly, much of their utility and flexibility can be attributed purely to two facts: they keep the suffixes sorted, and they expose the branching words in the string. By representing this information in a different way, we can get much of the benefit of suffix trees without the huge space cost. Readings:
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Range Minimum Queries, Part One
April 7
The range minimum query problem is the following: given an array, preprocess it so that you can efficiently determine the smallest value in a variety of subranges. RMQ has tons of applications throughout computer science and is an excellent proving ground for a number of advanced algorithmic techniques. Slides: Readings: |
Range Minimum Queries, Part Two
April 9
Our last lecture took us very, very close to a ⟨O(n), O(1)⟩-time solution to RMQ. Using a new data structure called a Cartesian tree in conjunction with a technique called the Method of Four Russians, we can adapt our approach to end up with a linear-preprocessing-time, constant-query-time solution to RMQ. In doing so, we'll see a number of clever techniques that will appear time and time again in data structure design. Slides: Readings:
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