| 1 |
Introduction |
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| 2 |
LINEAR PROGRAMMING (LP): basic notions, simplex metho |
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| 3 |
LP: Farkas Lemma, duality
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Problem set 1 due |
| 4 |
LP: complexity issues, ellipsoid method |
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| 5 |
LP: ellipsoid method |
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| 6 |
LP: optimization vs. separation, interior-point algorithm |
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| 7 |
LP: optimality conditions, interior-point algorithm (analysis) |
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| 8 |
LP: interior-point algorithm wrap up
NETWORK FLOWS (NF) |
Problem set 2 due |
| 9 |
NF: Min-cost circulation problem (MCCP) |
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| 10 |
NF: Cycle cancelling algs for MCCP |
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| 11 |
NF: Goldberg-Tarjan alg for MCCP and analysis |
Problem set 3 due |
| 12 |
NF: Cancel-and-tighten
DATA STRUCTURES (DS): Binary search trees
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| 13 |
DS: Splay trees, amortized analysis, dynamic trees |
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| 14 |
DS: dynamic tree operations |
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| 15 |
DS: analysis of dynamic trees
NF: use of dynamic trees for cancel-and-tighten
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| 16 |
APPROXIMATION ALGORITHMS (AA): hardness, inapproximability, analysis of approximation algorithms |
Problem set 4 due |
| 17 |
AA: Vertex cover (rounding, primal-dual), generalized Steiner tree |
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| 18 |
AA: Primal-dual alg for generalized Steiner tree |
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| 19 |
AA: Derandomization |
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| 20 |
AA: MAXCUT, SDP-based 0.878-approximation algorithm |
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| 21 |
AA: Polynomial approximation schemes, scheduling problem: P||Cmax |
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| 22 |
AA: Approximation Scheme for Euclidean TSP |
Problem set 5 due |
| 23 |
AA: Multicommodity flows and cuts, embeddings of metrics |
Problem set 6 due |