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## 4.1  Backjump Level And Bj K

backjump level Definition 6 (backjump level, Kondrak & van Beek, 1997)  The definition of backjump level is recursive:
1. A backjump from variable xi to variable xh is of level 1 if it is performed directly from a dead-end state in which every value of xi fails a consistency check.

2. A backjump from variable xi to variable xh is of level d ≥ if all backjumps performed to variable x i are of level less than d, and at least one of them is of level d –
Example 2  Figure 2 shows the backjump levels in an example CBJ backtrack tree.  There is a one-level backjump from x to x because every value in the domain of x fails a consistency check. Then CBJ finds two solutions for the problem and thus it chronologically backtracks from x  to x  , and later to x  . The backjumps are of level one and two respectively. At last there is a three-level backjump from x  to x .

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