6.5220/6.856J/18.416J Randomized Algorithms (Spring 2025)

Lecture: 2:30-4 Monday, Wednesday, Friday
Units: 5-0-7 G H-Level Grad Credit
Instructor: David Karger karger@mit.edu
TAs: Helen Shen junxuan@mit.edu
  Wei Zhang w_zhang@mit.edu
  Office hours: Monday 4-5PM Helen, Stata G5 Lounge
Friday 4-5PM Wei, Stata G5 Lounge

Course Announcements

Problem Sets

Set Due Dates Solutions Grading Supervisors Gradescope Code Peer Grading Sign-up Late Submission Form
PS 1 Wed, Sep. 10 Wei B3N3KJ PS 1 Graders PS 1 Late Form
PS 2 Wed, Sep. 17 Helen J6XE57 PS 2 Graders PS 2 Late Form

Lectures

Lecture Date Topic Notes Recording Scrawls
1 09/03 Introduction to Randomized Algorithms. Quicksort, BSP. NB L01 new, L01 L01
2 09/05 Min-cut, Complexity theory. NB L02 new, L02 L02
3 09/08 Adelman's theorem, Game tree evaluation. NB L03 new, L03 L03
4 09/10 Game theory, Lower bounds 1, Coupon collecting, Stable marriage NB L04 new, L04 L04
5 09/12 Deviations: Markov, Chebyshev. Median finding 1. NB L05 L05
6 09/15 Pseudorandom numbers. Chernoff bound. NB, NB L06 L06
7 09/17 Randomized routing. NB L07 L07
09/19 No lecture (Student Holiday)
8 09/22 The Power of Two Choices NB L08 L08
9 09/24 Hashing NB, NB L09 L09
10 09/26 Hashing 2 NB L10 L10
11 09/29 Fingerprinting NB L11 L11
12 10/01 Bloom Filters, Fingerprinting by polynomials, perfect matching. NB, NB L12 L12
13 10/03 Perfect matching, network coding, symmetry breaking. NB L13 L13
14 10/06 Symmetry breaking. Parallel algorithms. Independent set. NB L14 L14
15 10/08 Shortest Paths. NB L15 L15
16 10/10 Isolating Lemma. Perfect Matching. Shortest paths 1. NB L16 L16
10/13 No lecture (Indigenous Peoples' Day)
17 10/15 Sampling: polling. Streaming algorithms: frequent items, sketches, distinct items. NB, NB L17
18 10/17 Sampling: transitive closure. DNF counting, rare events. NB, NB L18 L18
19 10/20 Counting versus generation. Minimum spanning tree 1. NB L19 L19
20 10/22 Minimum spanning tree 2. Min-cuts: recursive contraction algorithm 1. NB, NB L20 L20
21 10/24 Min-cuts: recursive contraction algorithm 2. Sampling Minimum Cuts. NB L21 L21
22 10/27 Sampling Cuts NB L22 L22
23 10/29 Network reliability. NB L23 L23
24 10/31 Arrangements of lines. Convex hull via randomized incremental construction 1. NB L24 L24
25 11/03 Convex hull via randomized incremental construction 2. LP: sampling. NB, NB L25 L25
26 11/05 Sampling for LP. NB L26 L26
27 11/07 LP: simplex. Random Answers. NB, NB L27 L27
11/10 No lecture (Student holiday)
28 11/12 Randomized rounding. NB, NB L28 L28
29 11/14 Embeddings. NB L29
30 11/17 Metric Embeddings 2. NB L30
31 11/19 Metric Embeddings; Markov chains 1. NB, NB L31
32 11/21 Markov chains 2: random walks. NB L32
33 11/24 Markov chains 3. NB, NB L33
34 11/26 Markov chains 4. NB, NB L34
11/28 No lecture (Institute holiday)
35 12/01
36 12/03
37 12/05
38 12/08 Peer editing session. (Required attendance!!)
39 12/10 (Last day of classes)
Below this point is subject to change