Fail first principle

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The fail first principle is an idea of what a variable ordering heuristic should attempt to do in tree search. It suggests that the variable to be assigned next should be the one which is most likely to lead to a dead-end. The heuristic aims at proving that the search is in a sub-tree with no feasible solutions as soon as possible.

One way of operationalizing this principle, is to choose the next variable to assigned to be the variable which is the most constrained. The extent to which a variable is constrained can be measured in different ways. One simple measure being the current size of the domain. Under this measure, the variable which has the smallest domain should be assigned next. Another common measure is to select the variable that appears in the largest number of constraints. More sophisticated estimates exist.


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The tree formed by a branch and bound algorithm strategy. It is a tree because at each (forward) branching step the problem is partitioned into a disjunction. A common one is to dichotomize the value of some variable, LaTeX: \textstyle x \le v \mbox{ or } x \ge v + 1. This creates two nodes from the parent:

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