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Table 5 α k and execution time in network tomography problems

From: Computable performance guarantees for compressed sensing matrices

Matrix A

Algo.

α 1

α 2

α 3

α 4

α 5

k max

(a) α k values

33 × 66

1-Step TSA

0.28

0.41

0.50

0.57

0.62

2

 

2-Step TSA

0.28

0.41

0.50

0.57

0.62-0.64

2

 

3-Step TSA

0.28

0.41

0.50

0.57

0.62

2

53 × 105

1-Step TSA

0.20

0.29

0.36

0.45

0.52-0.54

4

 

2-Step TSA

0.20

0.29

0.36

0.45

0.49-0.56

4

 

3-Step TSA

0.20

0.29

0.36

0.45

0.52

4

(b) Execution time (Unit: second)

33 × 66

1-Step TSA

0.74

3.62

28.94

404.11

5.94e4

 
 

2-Step TSA

0.74

3.62

43.94

541.70

1 day

 
 

3-Step TSA

0.74

3.62

1.69e3

1.73e3

3.70e4

 
 

ESM

0.64

3.94

1.63e3

1.4e4a

1.8e5a

 

53 × 105

1-Step TSA

1.31

30.61

608.90

5.35e3

1 day

 
 

2-Step TSA

1.31

116.12

143.99

1.05e3

1 day

 
 

3-Step TSA

1.31

116.12

7.95e3

7.93e3

1.38e4

 
 

ESM

1.28

127.28

8.70.e3

9.6e4a

1.9e6a

 
  1. Random walk step: 20
  2. aExhaustive search method (estimated execution time = average time to solve (7) (=0.02 second) for an index set × total number of index sets)