Day |
Date |
Instr |
Topics Covered |
Notes and Readings |
Assignments |
Wed |
Sep 07 |
Gary |
Lecture 1: Introduction and Course topics, Introduced Graph Laplacian, Effective Resistance, and Random Walks |
ClassNotes-Intro - Doyle and Snell: Random Walks and Electric Networks
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Fri |
Sep 09 |
Gary |
Lecture 2: Resistance, Energy and Rayleigh's Monotonicity Law, and Commute Time |
ClassNotes-Intro
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Mon |
Sep 12 |
Gary |
Lecture 3: Random Walks on Graphs |
ClassNotes
|
|
Wed |
Sep 14 |
Gary |
Lecture 4: Mixing Rates for Random Walks |
ClassNotes - Lovasz Notes
|
|
Fri |
Sep 16 |
Gary |
Lecture 5: Bounding Eigenvalues and Symmetric Perron Frobenius for Laplacians using path embedding. |
ClassNotes - Spielman-3
|
|
Mon |
Sep 19 |
Gary |
Lecture 6: Bounding Eigenvalues, Courant-Fischer, and Path Embedding. |
ClassNotes - Spielman-4
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|
Wed |
Sep 21 |
Gary |
Lecture 7: Laplacians, Differential Equations, and Matrix Exponentials |
ClassNotes - Strang 5.4
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|
Fri |
Sep 23 |
Gary |
Lecture 8: Matrix Chernoff Bounds, Ahlswede-Winter, Tropp |
ClassNotes
- Golden-Thompson Notes
- Using AW
|
|
Mon |
Sep 26 |
Gary |
Lecture 9: Graph Sparsifiers and Ahlswede-Winter Thm |
ClassNotes - Spielman/Strivastava - Using AW
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|
Wed |
Sep 28 |
Gary |
Lecture 10: Golden-Thompson |
ClassNotes - VershyninNotes
|
|
Fri |
Sep 30 |
Gary |
Lecture 11: Solving Linear Systems: The Basic Iterative Method, Extrapolated Method, Chebyshev acceleration |
ClassNotes - Hageman and Young 3-4 - Saad 4-7
|
|
Mon |
Oct 03 |
Gary |
Lecture 12: Conjugate Gradient Method and Steepest Descent |
ClassNotes
- Trefethen and Bau Chapter 38
- Saad Chap 5
- Painless CG
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|
Wed |
Oct 05 |
Gary |
Lecture 13: Conjugate Gradient Method Continued |
|
|
Fri |
Oct 07 |
Gary |
Lecture 14: Preconditioned Conjugate Gradient Method and Low Stretch Spanning Trees |
ClassNotes
- Lecture 19 Spielman
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|
Mon |
Oct 10 |
|
CSC16 Conference - No Class |
|
|
Wed |
Oct 12 |
|
CSC16 Conference - No Class |
|
|
Fri |
Oct 14 |
Gary |
Lecture 15: Direct Linear Solvers" |
ClassNotes
- [CLRS Chap 28]
|
|
Mon |
Oct 17 |
Gary |
Lecture 16: Graph Cuts and Eigenvalues: Cheeger inequality |
ClassNotes
- Guattery's Notes
|
|
Wed |
Oct 19 |
Gary |
Lecture 17: Eigenvalues and Vectors by Iterative Methods |
ClassNotes
- Inverse Powering, see page 19
- Trefethen and Bau Chapter 27
|
|
Fri |
Oct 21 |
|
Midsemester Break - No Class |
|
|
Mon |
Oct 24 |
Gary |
Lecture 18: Continued: Eigenvalues and Vectors by Iterative Methods |
ClassNotes
- Inverse Powering, see page 19
- Trefethen and Bau Chapter 27
|
|
Wed |
Oct 26 |
Gary |
Lecture 19: Nested Dissection for Planar Graphs |
ClassNotes
- [CLRS Chap 28]
|
|
Fri |
Oct 28 |
|
Faculty Retreat - No Class |
|
|
Mon |
Oct 31 |
Gary |
Lecture 20: Fiedler's Thm and Generalized Laplacian's |
ClassNotes
- Spielman Lecture 7
- Godsil Royle Chap 13
|
|
Wed |
Nov 02 |
Gary |
Lecture 21: Arnoldi Iteration and Lanczos Algorithm |
ClassNotes - ClassNotesCont - Trefethen Bau Chap 33 - Trefethen Bau Chap 36
|
|
Fri |
Nov 04 |
Gary |
Lecture 22: Eigenvalues and vectors for Tridigonal Systems |
ClassNotes - Trefethen Bau Chap 30
|
|
Mon |
Nov 07 |
Gary |
Lecture 23: Graph Maximum Cut via Spectral |
ClassNotes - Williamson Lecture 8 - Williamson Lecture 9
|
|
Wed |
Nov 09 |
Gary |
Lecture 24: Solving Graph Laplacians in Nearly O(m log n) time |
ClassNotes - CACM
|
|
Fri |
Nov 11 |
Gary |
Lecture 25: Open Dicussion with Lorenzo Orecchia |
[His talk is at 3PM in 8102]
|
|
Mon |
Nov 14 |
Gary |
Lecture 26: Solving Symmetric Diagonally Dominate |
ClassNotes
|
|
Wed |
Nov 16 |
Gary |
Lecture 27: Random Walks and Matching |
ClassNotes
- Spielman Notes on Matching
|
|
Fri |
Nov 18 |
Gary |
Lecture 28: Symmetric Diagonally Dominate Solvers; Maximum Flow |
ClassNotes SDD - ClassNotes MaxFlow - Lee Rao Srivastava
|
|
Mon |
Nov 21 |
Gary |
Lecture 29: Maximum Flow via Electrical Flow Cont. |
OldClassNotes
|
|
Wed |
Nov 23 |
|
Thanksgiving - No Class |
|
|
Fri |
Nov 25 |
|
Thanksgiving - No Class |
|
|
Mon |
Nov 28 |
Gary |
Lecture 30: Counting and Generating Random Trees |
ClassNotes Counting - OldClassNotes Generating - Even Trees Chapter 2 - Broder Generating Random Spanning Tree - Aldous Generating Random Spanning Trees
|
|
Wed |
Nov 30 |
Gary |
Lecture 31: Computing Minimum Energy Flow |
ClassNotes - OldClassNotes - KOSZ Min Flow
|
|
Fri |
Dec 02 |
Gary |
Lecture 32: Faster Random Walks and Generating Random Spanning Trees |
OldClassNotes - Wilson: Generating Random Spanning Trees - Propp and Wilson: Generating Random Spanning Trees - Madry's Thesis, see Chap 7
|
|
Mon |
Dec 05 |
Shen Chen |
Lecture 33: Parallel Low Diameter Graph Decomposition using Delayed Start Times |
|
|
Wed |
Dec 07 |
Gary |
Lecture 34: Random Walks with Restarts and Spilling Paint |
Berkhin Painting - Andersen and Chung - ClassNotes - Spielman's Notes
|
|
Fri |
Dec 09 |
Gary |
Lecture 35: Random Walks with Restarts and Spilling Paint-continued |
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