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Backtracking is a class of algorithms for finding solutions to some computational problems, notably constraint satisfaction problems, that incrementally builds candidates to the solutions, and abandons a candidate ("backtracks") as soon as it determines that the candidate cannot possibly be completed to a valid solution.
The DPLL algorithm enhances over the backtracking algorithm by the eager use of the following rules at each step: Unit propagation If a clause is a unit clause, i.e. it contains only a single unassigned literal, this clause can only be satisfied by assigning the necessary value to make this literal true. Thus, no choice is necessary.
The most-used techniques are variants of backtracking, constraint propagation, and local search. These techniques are used on problems with nonlinear constraints. Variable elimination and the simplex algorithm are used for solving linear and polynomial equations and inequalities, and problems containing variables with infinite domain.
When further backtracking or backjumping from the node, the variable of the node is removed from this set, and the set is sent to the node that is the destination of backtracking or backjumping. This algorithm works because the set maintained in a node collects all variables that are relevant to prove unsatisfiability in the leaves that are ...
Backtracking algorithms work by choosing an unassigned variable and recursively solve the problems obtained by assigning a value to this variable. Whenever the current partial solution is found inconsistent, the algorithm goes back to the previously assigned variable, as expected by recursion.
In backtracking algorithms, look ahead is the generic term for a subprocedure that attempts to foresee the effects of choosing a branching variable to evaluate one of its values. The two main aims of look-ahead are to choose a variable to evaluate next and to choose the order of values to assign to it.
An argument against the use of Backtracking line search, in particular in Large scale optimisation, is that satisfying Armijo's condition is expensive. There is a way (so-called Two-way Backtracking) to go around, with good theoretical guarantees and has been tested with good results on deep neural networks, see Truong & Nguyen (2020). (There ...
The Dancing Links algorithm solving a polycube puzzle. In computer science, dancing links (DLX) is a technique for adding and deleting a node from a circular doubly linked list. It is particularly useful for efficiently implementing backtracking algorithms, such as Knuth's Algorithm X for the exact cover problem. [1]