An Exact Algorithm for Bilevel 0-1 Knapsack Problems

Table 4

Backtracking procedure for the follower and leader of BKP₁.

	𝑘
	1		2		3		4		1	2	3
𝜗/𝛽	𝑓^21(𝛽)	𝑓^11(𝛽)	𝑓^22(𝛽)	𝑓^12(𝛽)	𝑓^23(𝛽)	𝑓^13(𝛽)	𝑓^24(𝛽)	𝑓^14(𝛽)	𝑓^11(𝜗)	𝑓^12(𝜗)	𝑓^13(𝜗)
0	0	0	0	0	0	0	0	0	(0)	(0)	0
1	2	(5)	2	(5)	3	2	3	2	−∞	2	2
2	2	5	2	5	5	(7)	5	(7)	−∞	−∞	(7)
3	2	5	4	6	5	7	5	7	3	3	9
4	2	5	4	6	7	8	7	8	−∞	5	5