Lecture Schedule and Notes
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Date |
Topics
and Lecture Notes (Required
Readings and Lectures in Bold) |
Required
Readings in Bold (from
[CLRS] unless otherwise noted) |
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Tues, Aug 18 Zoom Lecture 1 by Prof John Reif (Assignment
of HM1: Asymptotic Notation and Recurrence) |
Overview of the course: Introduction to Algorithms: Optional Notes: (SS) analyzing algorithms (JR) Models of Computation [PDF] |
[CLRS 1 & 2], [DPV 0] Optional: |
|
Wends, Aug 19 Zoom Review by TA Xin Song |
Introduction
Recitation: (DF) Intro [PDF] Math
review, LaTeX, Average Case Analysis Insertion Sort and Mergesort |
[CLRS 3], [DPV 0] |
|
Thurs, Aug 20 Zoom Lecture 2 by Prof John Reif |
Asymptotic Analysis: (JR) Asymptotics and Recurrence Equations [PDF] Optional Notes on Asymptotic Analysis: |
[CLRS 3], [DPV 0] [GKP 2.5] |
|
Tues, Aug 25 Zoom Lecture 3 by Prof John Reif |
Recurrence Equations: (JR) Asymptotics and
Recurrence Equations [PDF] Optional Notes on Recurrence Equations: (SS) recurrence relations |
[CLRS 4.3-4.6], [DPV 2.2] |
|
Wends, Aug 26 Zoom Review by TA Xin Song (HM1 11:55pm
tonight) (Assignment
of HM2) |
Divide
and Conquer: A Case Study in
Strassen’s Matrix Multiplication Algorithm |
[CLRS 4.1-4.2], [DPV 2] (review
Strassen’s algorithm) |
|
Thurs, Aug 27 Zoom Lecture 4 by Prof John Reif |
Divide and Conquer: (DL) Divide and Conquer Merge sort, binary search,
powering a number, polynomial multiplication, matrix multiplication,
Fibonacci (BF) Matrix Multiplication via Divide and Conquer Optional Notes on Divide and Conquer: |
[CLRS 4.1-4.2], [DPV 2] |
|
Tues, Sept 1 Zoom Lecture 5 by Prof John Reif |
Sorting Algorithms: (DL) Linear time sorting Lower bounds on comparison-based sort, decision-tree model, comparison sort, radix sort Optional Notes on Linear Sorting: (SS) Linear Sorting Optional Notes on Lower Bounds on
Sorting: (LA) Lower bound in decision
tree model, bucket and radix sort (SS) Heapsort |
[CLRS 8] |
|
Wends, Sept 2 Zoom with TA Xin Song |
Quiz
on Asymptotic Notation and Recurrences |
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Thurs, Sept 3 Zoom
Lecture 6 by Prof John Reif |
Search Trees: Binary search trees - Balanced BSTs - Red-Black trees Optional Notes on Search Trees: (DL) Binary search trees - Expected Height Randomly Build Binary search trees (LA) Search trees, red-black
trees Optional: Skip Lists: (DL) Skip Lists Randomized Insertion & Analysis Further Dynamic
Data Structures (to be
presented by TA in Recitation): (DL) Augmenting Data Structures Dynamic Order Statistics, Interval Trees Optional Notes on Skip Lists: (LA) Hashing, Skip Lists |
[CLRS 12 & 13] |
|
*Tues, Sept 8 Zoom Lecture 7 by Prof John Reif |
Randomized
Algorithms and Quicksort: (PI) Randomized Algorithms and QuickSort Randomized algorithms: Monte-Carlo vs. Las-Vegas; matrix product checker; quick sort: deterministic, randomized; indicator variables, expected running time. Optional Notes on Quicksort: (LA) Quicksort Optional Notes on Randomized and
Average-Case Analysis: Optional Notes on Hidden Markov Models: (PI) Hidden Markov Models I Markov Chains, Hidden Markov Models, Dishonest Casino Example,
Evaluating path emissions likelihood, Max-likelihood path and Viterbi
algorithm, total emissions probability and forward algorithm. (PI) Hidden Markov Models II Algorithms
for HMMs: review of evaluation, Viterbi, forward; posterior decoding;
supervised learning; unsupervised learning: viterbi
training and baum-welch training. (PI) Computational Biology:
Regulatory Motif Discovery Bio intro: DNA and the
dynamic cell, Regulatory motif definitions, Combinatorial formulation: median
string finding, Probabilistic formulation: expectation maximization and Gibbs
sampling, comparative genomics and discovery by genome-wide conservation. |
[CLRS 7] |
|
Wends, Sept 9 Zoom Review by TA Xin Song (HM2 11:55pm
tonight) (Assignment
of HM3) |
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Thurs, Sept 10 Zoom Lecture 8 by Prof John Reif |
Selection Algorithms: Finding ith smallest element, probabilistic order statistic finder, deterministic linear-time select Optional Notes on Selection: (LA) Linear time selection,
median lower bound |
[CLRS 9] |
|
Tues, Sept 15 Zoom Lecture 9 by Prof John Reif |
Introduction to Hashing: (DL) Hashing
I Simple uniform hashing, open
addressing (BF) Consistent
Hashing Optional Notes Introducing Hashing: (SS) Introduction to Hash
Tables Optional
References on Consistent Hashing: (TR&GV) Consistent
Hashing (David
Karger, et al.) Akamai
Consistent Hashing Paper |
[CLRS 11] |
|
Wends, Sept 16 Zoom Review by TA Xin Song |
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|
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Thurs, Oct 17 Zoom Lecture 10 by Prof John Reif |
Universal Hashing: (DL) Hashing II Universal
hashing, perfect hashing
Optional Notes on Universal Hashing and Extensions: (EU) Universal Hashing (SS) elementary data structures (JR) Hashing Polynomials |
[CLRS 11] |
|
Tues, Sept 22 Zoom Lecture 11 by Prof John Reif |
Computational
Geometry (PI) Closest Pair in 2D
(PI) Computational Geometry - Segment Intersection Optional
Reading for Locality Sensitive Hashing:
(BF) Locality Sensitive Hashing: Approximate Nearest Neighbor
in High Dimension (Alexander Andoni and PI) Survey
Article from Communications of the ACM (KM) Locality
Sensitive Hashing (TR&GV) Dimensionality
Reduction |
[CLRS 33] |
|
Wends, Sept 23 Zoom Review by TA Xin Song (HM3 11:55pm
tonight) (Assignment
of HM4) |
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Thurs, Sept 24 Zoom Lecture 12 by Prof John Reif |
Computational
Geometry, Cont: (JRJ)
Convex Hull [PPT] [PDF] |
[CLRS 33] |
|
Tues, Sept 29 Zoom Lecture
13 by Prof John Reif |
Amortized
Analysis: (DL) Amortized Analysis I Dynamic
Tables, Accounting and Potential Methods (EU) Amortized Analysis Optional Notes on Amortized Analysis: (PI) Amortized Analysis
II Find-union data
structure - amortized analysis (DL) Competitive Analysis Self-Organizing Lists |
[CLRS 17] |
|
Wends, Sept 30 Zoom with TA Xin Song |
Midterm Exam (Sorting, Searching, Hashing, Randomized
Analysis) |
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Thurs, Oct 1 Zoom Lecture 14 by Prof John Reif |
Fast Fourier Transform and Polynomial Algorithms (PI) Fast
Fourier Transform Fast
Fourier Transform - Polynomial multiplication Optional Notes on Fast Fourier
Transform and Polynomial Algorithms:\ |
[CLRS 30], [DPV 2.5,2.6] |
|
Tues, Oct 6 Zoom Lecture 15 by Prof John Reif |
Number Theory and Cryptography
Algorithms: (EU) Public Key Cryptography and Number Theory
Algorithms Optional Notes on Cryptography: (BF) Bit-Coin
and Cryptographic Hashing |
[CLRS 31] |
|
Tues, Oct 7 Zoom Review by TA Xin Song (HM4 11:55pm
tonight) (Assignment
of HM5) |
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Thurs, Oct 8 Zoom Lecture 16 by Prof John Reif |
Pattern Matching: (PI)Randomized Pattern Matching Pattern
matching - average case analysis - Karp-Rabin algorithm – fingerprinting Optional Notes on Pattern Matching: |
[CLRS 32] |
|
Tues, Oct 13 Zoom Lecture 17 by Prof John Reif |
Introduction to Graphs and Their Data Structures: (SS) Data structures for graphs Optional Notes on Graph Definitions: Optional Notes on Depth First Search (LA) Model, basic algorithms,
DFS, BFS, topological sort, strongly connected components |
[CLRS 22], [DPV 3] |
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Wends, Oct 14 Zoom Review by TA Xin Song |
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|
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Thurs, Oct 15 Zoom Lecture 18 by Prof John Reif |
Introduction to Graph Algorithms (Depth First
Search): (JR) Graph Algorithms using Depth First Search [PDF] Optional Notes on Depth First Search (LA) Model, basic algorithms,
DFS, BFS, topological sort, strongly connected components |
[CLRS 22], [DPV 3] |
|
Tues, Oct 20 Zoom Lecture 19 by Prof John Reif |
(DL) Greedy Algorithms (and Graphs) (LA) Minimum
spanning trees, Union-Find Optional Notes: (EU) Minimum Weights Spanning
Tree |
[CLRS 16.0-16.3 & 23], [DPV 5] |
|
Tues, Oct 21 Zoom Review by TA Xin Song (HM5 11:55pm
tonight) (Assignment
of HM6) |
Lossless
Compression: Huffman Encoding (BF)
Huffman Encoding Optional Notes on Lossless
Encoding: |
|
|
Thurs, Oct 22 Zoom Lecture 20 by Prof John Reif |
Graph algorithms (Single Source Shortest Paths): Multiple Source Shortest Paths: (DL) Shortest Paths II Negative
weights and lack of greedy-choice property; Bellman-Ford. (DL) All Pair Shortest Paths All-pairs
shortest paths and dynamic programming, matrix multiplication, Floyd-Warshall; Johnson's algorithm, graph reweighing and
difference constraints. Optional Notes on Shortest Paths: Further Shortest
Paths Algorithms: Shortest Paths Algorithms for Graphs
with Negative Weights: (LA) Shortest paths |
[CLRS 24], [CLRS
25] ,
[DPV 4] |
|
Tues, Oct 27 Zoom Lecture 21 by Prof John Reif |
Augmenting Paths (Graph
Matching): Optional Notes on Graph Matching: Optional Notes on Network flow:
(further application of augmenting paths) (PI) Network Flows I Network flows - max flow - cut - residual graph - augmenting
paths Further Flow
Algorithms (to be presented in
Recitation): (PI) Network Flows II Network flows - Ford-Fulkerson algorithm - Edmonds-Karp Algorithm Further Optional Notes on Network Flows: (JR) Flow Algorithms [PDF] |
[CLRS 22.1-22.2], [DPV 7.3] Optional reading: [CLRS 26.1-26.2], [DPV 7.2] |
|
Wends, Oct 28 Zoom with Xin Song |
Exam
(Computational Geometry, Amortized Analysis, FFT,
Cryptography, Pattern Matching) |
|
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Thurs, Oct 29 Zoom Lecture 22 by Prof John Reif |
(DL) Dynamic Programming:
Dynamic Programming Hallmarks; Overlapping subproblems, Re-use of
computation, Bottom-Up; Longest Common Subsequence, recursive formulation,
proof of optimal substructure, traceback (LA) Dynamic
Programming, Matrix chain multiplication Optional Notes: |
[CLRS15], [DPV 6] |
|
Tues, Nov 3 Zoom Lecture 23 by Prof John Reif |
Combinatorial Search Problems: Approximation Algorithms for NP Search Problems: (PI) NP Search Problems and Approximation
Algorithms Optional Notes on Approximation Algorithms |
[CLRS 34 & 35], [DPV 8] |
|
Wends, Nov 4 Zoom Review by TA Dan Fu (HM6 11:55pm
tonight) (Assignment
of HM7) |
(PI) NP - Reductions (Pearsaul) NP
and NP Completeness |
|
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Thurs, Nov 5 Zoom Lecture 24 by Prof John Reif |
Algorithms
for Big Data, I: External Memory Algorithms: (LA) Model, basic upper and lower bounds,
sorting, B-tree Optional Notes on External Memory
Algorithms: |
[CLRS
16.3], [DPV 5.2] |
|
Tues, Nov 10 Zoom Lecture 25 by Prof John Reif |
Algorithms
Applied to WWW, I: PageRank (BF) Measuring Web Graph
Centrality: The PageRank Algorithm Optional Lectures on Algorithms
Applied to WWW: Spectral Graph
Algorithms: (BF) Intro to Spectral Techniques: Graphs and
Eigenvalues (BF) Spectral Clustering in Graphs |
[CLRS 18] |
|
Weds, Nov 11 Zoom Review by TA Xin Song |
Late
Term Exam (Graph Algorithms, Greedy Algorithms, Matching, Dynamic
Programming, Approximation Algorithms) |
|
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Thurs, Nov 12 Zoom Lecture 26 by Prof John Reif |
Algorithms
for Big Data, II: Streaming
Algorithms: Bloom Filters and Counting Distinct Elements (MG) Intro
to Streaming Algorithms [PPT] [PDF] (BF) Streaming Algorithms: CountMin-Sketch Optional Lectures on Streaming Algorithms (RJ) Streaming Algorithms
Overview [PPT] [PDF] |
|
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Wends, Nov 18 Zoom Review by TA Xin Song (HM7 11:55pm
tonight) |
Final Exam Review Notes on Final Exam Review (read before you take
the final exam): (BF) Final Exam Review |
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Sunday,
Nov 22 7:00
PM – 10:00 PM |
FINAL EXAM (see schedule of final exams for
TTH, Period 3) |
Credits for lecture notes:
- (HE) Herbert Edelsbrunner - graduate level notes with detailed
technical explanations.
- (BF) Brandon Fain - lecture
notes.
- (DF) Dan Fu - lecture notes.
- (MG) Minos Garofalakis - lecture notes.
- (RJ) Rahul Jain- lecture notes.
- (PI) Piotr Indyk - lecture notes based on CLRS Textbook.
- (RJ) Rahul Jain- lecture notes
- (JRJ) Jehn-Ruey Jiang - lecture notes.
- (DL) Erik
Demaine and Charles Leiserson undergraduate level lecture notes by CLRS
Textbook author.
- (ML) Michael Littman – low level undergraduate lecture notes.
- (JR) John H Reif – detailed lecture notes covering many algorithm
techniques.
- (SS) Steven Skiena - lecture notes with lots of graphics.
- (DS) Dan Sleator - brief lecture notes.
- (EU) Eli Upfal - lecture
notes with terse proofs.
- (JV) Jeff Vitter – survey papers on external memory model.
- (LY) Li Yang – introduction to cryptography
Course textbooks:
- [CLRS] Cormen, Leiserson, Rivest, and Stein. Introduction
to Algorithms, McGraw Hill, third edition, 2009. Be sure to get the third
edition!
- [DPV] Dasgupta, Papadimitriou, and Vazirani. Algorithms,
McGraw-Hill, first edition, 2006. (ISBN: 0073523402)
Other references made available:
- [Baase] Sara Baase. Computer Algorithms,
Introduction to Design and Analysis.
- [GKP] Ron
Graham, Donald Knuth, and Oren Patashnik. Concrete Mathematics.
- [GT]
Michael. T. Goodrich and Roberto Tamassia. Data Structures and Algorithms
in Java.
- [Kozen] Dexter C. Kozen. The Design and Analysis of
Algorithms.
- [MR] Rajeev
Motwani Prabhakar Raghavan. Randomized
Algorithms.