Dataset

Costvector
 


〈−1,1,1,1〉

〈0,1,2,1〉

〈0,2,3,1〉



k
/
k
^{′}

#
A
C
/
#
A
C
^{′}

#
T
/
#
T
^{′}

k
/
k
^{′}

#
A
C
/
#
A
C
^{′}

#
T
/
#
T
^{′}

k
/
k
^{′}

#
A
C
/
#
A
C
^{′}

#
T
/
#
T
^{′}


EC

3/3

2/2

2/2

3/3

18/16

18/16

3/3

16/16

16/16

GL

4/4

2/2

2/2

4/4

2/2

2/2

4/4

2/2

2/2

SC

6/6

1/1

1/1

6/6

1/1

1/1

6/6

1/1

1/1

RP

9/9

2/2

3/3

8/8

2/2

8/8

2/2

2/2

3/3

PMP

6/6

2/2

2/2

6/6

2/2

2/2

5/5

11/4

11/4

PML

5/5

2/2

2/2

5/5

2/2

2/2

3/3

18/6

18/6

PP

4/4

144/96

144/96

4/4

72/48

72/48

4/4

72/48

72/48

FD

9/10

576/240

944/512

9/9

276/4

408/8

−

−

−

COG2085

14/14

82560/9408

109056/9408

14/14

37088/4032

37568/4032

14/14

46656/5184

46656/5184

COG4965

16/16

31448/15744

44800/22400

16/16

640/320

640/320

13/16

5120/2560

6528/3328

 For some datasets, the number of optimal timefeasible solutions may be huge when k is unbounded. In some cases, however, by introducing a bound on k we can greatly reduce the number of timefeasible solutions while keeping their optimality. For all datasets whose number of acyclic solutions is positive for unbounded k, we identified k
_{
start
} (minimum k whose optimal cost is equal to the optimal cost obtained for unbounded k) and we searched for the minimum k
^{′}≥k
_{
start
} whose number of acyclic solutions is non zero. We executed this procedure for every pair (dataset, cost vector) for which the number of optimal acyclic solutions is positive. In the first column, the values for k=k
_{
start
} and k
^{′} are given. #
A
C/#
A
C
^{′} denotes the number of optimal acyclic solutions for the case when the switches are unbounded and the case when they are bounded by k
^{′}, respectively. The same relation is shown for the total number of optimal solutions in the column #
T/#
T
^{′}.