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# Table 3 Searching for time-feasible solutions by varyingk

Dataset Costvector
〈−1,1,1,1〉 〈0,1,2,1〉 〈0,2,3,1〉
k start →k A $$\boldsymbol {o \rightarrow o_{k_{A}}}$$ #A k start →k A $$\boldsymbol {o \rightarrow o_{k_{A}}}$$ #A k start →k A $$\boldsymbol {o \rightarrow o_{k_{A}}}$$ #A
SFC 7→6 6→7 16 7→6 21→22 16 7→5 31→35 12
RH 6→5 8→12 16 6→5 43→48 192 6→5 62→68 48
COG3715 13→12 10→11 288 22→6 51→176 6 22→6 80→206 2
COG4964 22→4 20→208 30 13→12 33→34 288 13→12 49→50 288
1. For some datasets (SFC, RH, COG3715 and, COG4964), the number of optimal time-feasible solutions is zero when reconciliations are obtained by using a given cost vector and unbounded k. After identifying k start (minimum k whose optimal cost o is equal to the optimal cost obtained for unbounded k), we decremented k until k A (maximum k which generates acyclic solutions) is found. For each pair (dataset, cost vector), the following values are given: the decrement of the bound (from k start to k A ), the new optimum found (from o to o A ) and the new number of acyclic solutions (# A). 