Table 3.

Searching for time-feasible solutions by varying k

Dataset	Costvector
	〈−1,1,1,1〉			〈0,1,2,1〉			〈0,2,3,1〉
	k start →k A	$o\to o_{k_A}$	#A	k start →k A	$o\to o_{k_A}$	#A	k start →k A	$o\to o_{k_A}$	#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

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).