# Table 4 Reducing the number of optimal time-feasible solutions by boundingk

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
1. For some datasets, the number of optimal time-feasible 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 time-feasible 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 .