21. Dijkstra’s Algorithm to Generate Single Source Shortest Paths
22. The Single-Source Shortest Path Problem
23. An Example for Prim’s Algorithm
24. ** after Algorithm_greedy.pptx
25. Two Feasible Solutions
26. The 2-terminal One to Any Special Channel Routing Problem
27. Gaussian elimination
28. Step 2:How to find all cycles in a graph?[Reingold, Nievergelt and Deo 1977]How many cycles are there in a graph in the worst case?In a complete digraph of n vertices and n(n-1) edges:Step 3:How to check if a cycle is a linear combination of some cycles?U
29. Gaussian elimination
30. The 2-terminal One to Any Special Channel Routing Problem
31. Two Feasible Solutions
32. ** after Algorithm_greedy.pptx
33. Two Feasible Solutions
34. Redrawing Solutions
35. At each point, the local density of the solution is the number of lines the vertical line intersects.The problem: to minimize the density. The density is a lower bound of the number of tracks.Upper row terminals: P1 ,P2 ,…, Pn from left to right.Lower ro
36. Suppose that we have the minimum density d of a problem instance. We can use the following greedy algorithm: Step 1 : P1 is connected Q1. Step 2 : After Pi is connected to Qj, we check whether Pi+1 can be connected to Qj+1. If the density is incre
37. Slide 41
38. The knapsack Problem
39. Slide 43
40. The knapsack algorithm
41. ** after Algorithm_greedy.pptx
42. The knapsack algorithm
43. Slide 43
44. The knapsack Problem
45. Slide 41
46. Suppose that we have the minimum density d of a problem instance. We can use the following greedy algorithm: Step 1 : P1 is connected Q1. Step 2 : After Pi is connected to Qj, we check whether Pi+1 can be connected to Qj+1. If the density is incre
47. At each point, the local density of the solution is the number of lines the vertical line intersects.The problem: to minimize the density. The density is a lower bound of the number of tracks.Upper row terminals: P1 ,P2 ,…, Pn from left to right.Lower ro
48. Redrawing Solutions
49. Two Feasible Solutions
50. The 2-terminal One to Any Special Channel Routing Problem
51. Gaussian elimination
52. Step 2:How to find all cycles in a graph?[Reingold, Nievergelt and Deo 1977]How many cycles are there in a graph in the worst case?In a complete digraph of n vertices and n(n-1) edges:Step 3:How to check if a cycle is a linear combination of some cycles?U
53. Detailed Steps for the Minimal Cycle Basis Problem
54. A greedy algorithm for finding a minimal cycle basis:Step 1: Determine the size of the minimal cycle basis, denoted as k.Step 2: Find all of the cycles. Sort all cycles by weights.Step 3: Add cycles to the cycle basis one by one. Check if the added cycle
55. Slide 31
56. Slide 30
57. The minimal cycle basis problem
58. An example of Huffman algorithm
59. Huffman codes
60. Slide 26
61. An example of 2-way merging
62. A Greedy Algorithm to Generate an Optimal 2-Way Merge Tree
63. Slide 23
64. Linear Merge Algorithm
65. Slide 21
66. Slide 20
67. Slide 21
68. Linear Merge Algorithm
69. Slide 23
70. A Greedy Algorithm to Generate an Optimal 2-Way Merge Tree
21. Dijkstra’s Algorithm to Generate Single Source Shortest Paths
22. The Single-Source Shortest Path Problem
23. An Example for Prim’s Algorithm
24. ** after Algorithm_greedy.pptx
25. Two Feasible Solutions
26. The 2-terminal One to Any Special Channel Routing Problem
27. Gaussian elimination
28. Step 2:How to find all cycles in a graph?[Reingold, Nievergelt and Deo 1977]How many cycles are there in a graph in the worst case?In a complete digraph of n vertices and n(n-1) edges:Step 3:How to check if a cycle is a linear combination of some cycles?U
29. Gaussian elimination
30. The 2-terminal One to Any Special Channel Routing Problem
31. Two Feasible Solutions
32. ** after Algorithm_greedy.pptx
33. Two Feasible Solutions
34. Redrawing Solutions
35. At each point, the local density of the solution is the number of lines the vertical line intersects.The problem: to minimize the density. The density is a lower bound of the number of tracks.Upper row terminals: P1 ,P2 ,…, Pn from left to right.Lower ro
36. Suppose that we have the minimum density d of a problem instance. We can use the following greedy algorithm: Step 1 : P1 is connected Q1. Step 2 : After Pi is connected to Qj, we check whether Pi+1 can be connected to Qj+1. If the density is incre
37. Slide 41
38. The knapsack Problem
39. Slide 43
40. The knapsack algorithm
41. ** after Algorithm_greedy.pptx
42. The knapsack algorithm
43. Slide 43
44. The knapsack Problem
45. Slide 41
46. Suppose that we have the minimum density d of a problem instance. We can use the following greedy algorithm: Step 1 : P1 is connected Q1. Step 2 : After Pi is connected to Qj, we check whether Pi+1 can be connected to Qj+1. If the density is incre
47. At each point, the local density of the solution is the number of lines the vertical line intersects.The problem: to minimize the density. The density is a lower bound of the number of tracks.Upper row terminals: P1 ,P2 ,…, Pn from left to right.Lower ro
48. Redrawing Solutions
49. Two Feasible Solutions
50. The 2-terminal One to Any Special Channel Routing Problem
51. Gaussian elimination
52. Step 2:How to find all cycles in a graph?[Reingold, Nievergelt and Deo 1977]How many cycles are there in a graph in the worst case?In a complete digraph of n vertices and n(n-1) edges:Step 3:How to check if a cycle is a linear combination of some cycles?U
53. Detailed Steps for the Minimal Cycle Basis Problem
54. A greedy algorithm for finding a minimal cycle basis:Step 1: Determine the size of the minimal cycle basis, denoted as k.Step 2: Find all of the cycles. Sort all cycles by weights.Step 3: Add cycles to the cycle basis one by one. Check if the added cycle
55. Slide 31
56. Slide 30
57. The minimal cycle basis problem
58. An example of Huffman algorithm
59. Huffman codes
60. Slide 26
61. An example of 2-way merging
62. A Greedy Algorithm to Generate an Optimal 2-Way Merge Tree
63. Slide 23
64. Linear Merge Algorithm
65. Slide 21
66. Slide 20
67. Slide 21
68. Linear Merge Algorithm
69. Slide 23
70. A Greedy Algorithm to Generate an Optimal 2-Way Merge Tree
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