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Backjumping : ウィキペディア英語版
Backjumping
In backtracking algorithms, backjumping is a technique that reduces search space, therefore increasing efficiency. While backtracking always goes up one level in the search tree when all values for a variable have been tested, backjumping may go up more levels. In this article, a fixed order of evaluation of variables x_1,\ldots,x_n is used, but the same considerations apply to a dynamic order of evaluation.

Image:Backtracking-no-backjumping.svg|A search tree visited by regular backtracking
Image:Backtracking-with-backjumping.svg|A backjump: the grey node is not visited

==Definition==

Whenever backtracking has tried all values for a variable without finding any solution, it reconsiders the last of the previously assigned variables, changing its value or further backtracking if no other values are to be tried. If x_1=a_1,\ldots,x_k=a_k is the current partial assignment and all values for x_ have been tried without finding a solution, backtracking concludes that no solution extending
x_1=a_1,\ldots,x_k=a_k exists. It then "goes up" to x_k, changing its value if possible, backtracking again otherwise.
The partial assignment is not always necessary in full to prove that no value of x_ lead to a solution. In particular, a prefix of the partial assignment may have the same property, that is, there exists an index j such that x_1,\ldots,x_j=a_1,\ldots,a_j cannot be extended to form a solution with whatever value for x_. If the algorithm can prove this fact, it can directly consider a different value for x_j instead of reconsidering x_k as it would normally do.
The efficiency of a backjumping algorithm depends on how high it is able to backjump. Ideally, the algorithm could jump from x_ to whichever variable x_j is such that the current assignment to x_1,\ldots,x_j cannot be extended to form a solution with any value of x_. If this is the case, j is called a ''safe jump''.
Establishing whether a jump is safe is not always feasible, as safe jumps are defined in terms of the set of solutions, which is what the algorithm is trying to find. In practice, backjumping algorithms use the lowest index they can efficiently prove to be a safe jump. Different algorithms use different methods for determining whether a jump is safe. These methods have different cost, but a higher cost of finding a higher safe jump may be traded off a reduced amount of search due to skipping parts of the search tree.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
ウィキペディアで「Backjumping」の詳細全文を読む



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