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Advanced Algorithms
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CS520 at IITG by R. Inkulu
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Introduction
[WS]: 3-5; [more]
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Greedy apprx
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Metric k-center clustering
[WS]: 30-32
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Set cover
[WS]: 15-17
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Shortest superstring
[note]
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Minimizing the maximum lateness
[WS]: 28-30
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Minimizing the makespan
[WS]: 34-35; [note]
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Minimum cost Steiner tree
[Vaz]: 27-30
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Metric TSP
[WS]: 35-40
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Local search based apprx
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Minimizing the makespan
[WS]: 32-34
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Max cut
[KT]: 676-679
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Maximum independent set of disks
[note]
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Minimum degree spanning tree
[WS]: 43-46
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Vizing's edge coloring
[WS]: 47-51
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Metric uncapacitated facility location
[WS]: 232-238
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Metric k-median clustering
sketched [WS]: 238-242 --- AR
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Apprx using grids
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Point set diameter
[note]
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Smallest k-enclosing disk
[PelMaz '05]: 3-5
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Covering with disks: Hochbaum-Mass shifting
[P]: 151-153
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Apprx with dynamic programming
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Knapsack
[WS]: 57-61
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Minimizing the makespan
[WS]: 61-66
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Bin-packing
[WS]: 66-70
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Arora's PTAS for Euclidean TSP
[WS]: 255-267
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Mitchell's guillotine cuts
[Mitch '99]: 2-8
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Randomized approximation
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Las Vegas algorithms for max SAT and max cut
[WS]: 100-102, 104-106; [more]
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Derandomization via conditional expectations: max SAT
[WS]: 103-104
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Rounding and the power of two choices: max SAT
[WS]: 106-112
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An ADO for weighted undirected graphs
[ThoZwi '05]: 7-10
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Monte Carlo algorithm for approximate median
[note]
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Iterative reweighing: geometric set cover
[Mnote]
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A few more techniques for apprx
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Isolating cuts: edge multiway cut
[WS]: 194-195
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Minimum k-cut using Gomory-Hu tree
[Vaz]: 40-44
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Baker's shifting technique for planar graphs
[wiki]; [note]
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Tree metrics: uniform buy-at-bulk
[WS]: 210-218
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Spanners for undirected graphs
[TS]
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A light apprx shortest path tree
[Khuller et al. '95]: 3-9
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LP rounding
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Intro to LP
[note] --- a review
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Set cover
[WS]: 9-14, 19-22
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A scheduling problem
[WS]: 74-78
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Prize-collecting Steiner tree
[WS]: 80-83, 113-116
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Metric uncapacitated facility location
[WS]: 83-88, 116-119
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Bin packing
[WS]: 88-93
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Max SAT
[WS]: 106-113
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Congestion minimization
[WS]: 128-129
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Hardness of approximation
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More gap introducing reductions
[WS]: 410-414
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Gap preserving reductions
parts of [WS]: 414-424
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Matchings
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Maximum weighted bipartite matching
[ScN]: 40-41, 45, 47-50
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Edmonds maximum cardinality matching
[ScN]: 81-84
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Minimum weight T-joins
[ChekN]
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Connectivity
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All-pairs minimum cuts: Gomory-Hu tree
[ChekN]; [GoemN]: 11-12
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Karger's algorithm for global minimum cut
[KT]: 714-719
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Karger-Klein-Tarjan's MST algorithm
[note]
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Brooks' theorem for vertex coloring
[W]: 197-198
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Edmonds' minimum cost arborescence
[KT]: 177-183
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Auslander & Parter's planarity testing algorithm
[Batti]: 74-81
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Lipton & Trajan's planar separator theorem
[Koz]: 77-83
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[WS]: The Design of Approximation Algorithms by David P. Williamson and David B. Shmoys.
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Additional resources/notes are posted where necessary.
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AR stands for additional reading (no lecture delivered but included in syllabus).