Honours Algorithm Design COMP-362
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1 Lecture Notes Page 1 Honours Algorithm Design COMP-362 Lecture notes by Alexandre Tomberg Prof. Patrick Hayden McGill University Fall 2008
2 Lecture Notes Page 2 Table of Contents December :16 PM
3 Lecture Notes Page 3
4 Lecture Notes Page 4 Dynamic Programming September :46 AM
5 Lecture Notes Page 5
6 Lecture Notes Page 6
7 Lecture Notes Page 7 String Theory September :57 AM
8 Lecture Notes Page 8
9 Lecture Notes Page 9 Approximation Algorithm December :43 PM
10 Lecture Notes Page 10
11 Lecture Notes Page 11 Dynamic Programming (in disguise) September :39 AM
12 Lecture Notes Page 12
13 Lecture Notes Page 13
14 Lecture Notes Page 14
15 Lecture Notes Page 15
16 Lecture Notes Page 16 Independent Set September :40 PM
17 Lecture Notes Page 17 Greedy Selection September :40 AM
18 Lecture Notes Page 18 Greedy Weighted Selection Given: While If then Return:
19 Lecture Notes Page 19
20 Lecture Notes Page 20
21 Lecture Notes Page 21 Introduction to Linear Programming September :39 AM
22 Lecture Notes Page 22 Solving Linear Programming Problems. Linear Programming in General.
23 Lecture Notes Page 23 Standard Form Duality
24 Lecture Notes Page 24
25 Lecture Notes Page 25
26 Lecture Notes Page 26 Flows October :39 AM
27 Lecture Notes Page 27 Cuts October :51 AM
28 Lecture Notes Page 28
29 Lecture Notes Page 29
30 Lecture Notes Page 30
31 Lecture Notes Page 31
32 Lecture Notes Page 32
33 Lecture Notes Page 33
34 Lecture Notes Page 34
35 Lecture Notes Page 35
36 Lecture Notes Page 36 Ford -Folkerson Algorithm September :37 PM Ford-Folkerson (G,s,t,c): While do: return Edmonds-Karp:
37 Lecture Notes Page 37
38 Lecture Notes Page 38
39 Lecture Notes Page 39 Applications of Max Flow September :08 PM
40 Lecture Notes Page 40
41 Lecture Notes Page 41
42 Lecture Notes Page 42
43 Lecture Notes Page 43
44 Lecture Notes Page 44 Symplex Algorithm October :39 AM
45 Lecture Notes Page 45
46 Lecture Notes Page 46
47 Lecture Notes Page 47
48 Lecture Notes Page 48
49 Lecture Notes Page 49
50 Lecture Notes Page 50
51 Lecture Notes Page 51
52 Lecture Notes Page 52 Max Flow & Simplex October :04 PM
53 Lecture Notes Page 53
54 Lecture Notes Page 54 Polytime algorithms October :37 PM
55 Lecture Notes Page 55
56 Lecture Notes Page 56 Circuit - Satisfiability (Sat) October :50 AM
57 Lecture Notes Page 57
58 Lecture Notes Page 58 NP-Complete problems October :35 PM
59 Lecture Notes Page 59
60 Lecture Notes Page 60 Independent Set October :42 AM
61 Lecture Notes Page 61
62 Lecture Notes Page 62 Vertex Cover October :08 PM
63 Lecture Notes Page 63 Hamiltonian Cycle October :19 PM
64 Lecture Notes Page 64
65 Lecture Notes Page 65
66 Lecture Notes Page 66 3D -matching October :29 PM
67 Lecture Notes Page 67
68 Lecture Notes Page 68 Integer Linear Programming October :19 PM
69 Lecture Notes Page 69
70 Lecture Notes Page 70 Subset Sum October :30 PM
71 Lecture Notes Page 71 Feed forward Neural Nets October :55 AM
72 Lecture Notes Page 72
73 Lecture Notes Page 73
74 Lecture Notes Page 74
75 Lecture Notes Page 75
76 Lecture Notes Page 76
77 Lecture Notes Page 77 Complement of NP October :04 PM
78 Lecture Notes Page 78 k-colorability October :39 AM
79 Lecture Notes Page 79 How to deal with NP-hardness October :48 AM
80 Lecture Notes Page 80
81 Backtrack (problem P) Lecture Notes Page 81
82 Lecture Notes Page 82 Branch & Bound (problem P): while choose expand for each if else if return (best)
83 Lecture Notes Page 83
84 Lecture Notes Page 84 Approximate solutions of Vertex Cover problem November :48 AM
85 Lecture Notes Page 85
86 Lecture Notes Page 86
87 Lecture Notes Page 87
88 Lecture Notes Page 88
89 Lecture Notes Page 89 Set Cover November :39 AM
90 Lecture Notes Page 90
91 Lecture Notes Page 91
92 Lecture Notes Page 92
93 Lecture Notes Page 93 k-cluster November :21 PM
94 Lecture Notes Page 94
95 Lecture Notes Page 95 Metric Traveling Salesman Problem November :45 PM
96 Lecture Notes Page 96 Approximability November :41 AM
97 Lecture Notes Page 97
98 Lecture Notes Page 98 Probabilistically Checkable Proofs (PCP) November :53 AM
99 Lecture Notes Page 99
100 Lecture Notes Page 100
101 Lecture Notes Page 101
102 Lecture Notes Page 102
103 Lecture Notes Page 103
104 Lecture Notes Page 104 Dealing with NP- hardness November :23 PM
105 Lecture Notes Page 105
106 Lecture Notes Page 106 Tree Width November :41 AM
107 Lecture Notes Page 107
108 Lecture Notes Page 108
109 Lecture Notes Page 109
110 Lecture Notes Page 110
111 Lecture Notes Page 111
112 Lecture Notes Page 112
113 Lecture Notes Page 113
114 Lecture Notes Page 114 Control-flow graphs November :19 PM
115 Lecture Notes Page 115 Finding Tree Decompositions November :31 PM
116 Lecture Notes Page 116 Final Exam November :25 PM
117 Lecture Notes Page 117 NPC Reductions Map December :03 AM
118 Lecture Notes Page 118 Computation & Time Travel November :41 AM
AN EXAMPLE OF THE GOMORY CUTTING PLANE ALGORITHM. max z = 3x 1 + 4x 2. 3x 1 x x x x N 2
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