P. Van Hentenryck and V. Ramachandran. Backtracking without Trailing in CLP(R Lin ). Proc. ACM-SIGPLAN Conference on Programming Language Design and Implementation. 349--360. 1994.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....requires incremental checks of the satisfiability of a system of equations and inequalities. Experience has shown that Gauss Jordan elimination and the simplex method are efficient enough to be of practical value in the implementation of CLP languages based on linear arithmetic constraints [1, 2, 4, 6, 7, 8]. However, these algorithms must be modified to accommodate the special demands of CLP execution. First, they must be applied incrementally. Secondly, they must co exist with backtracking. An added consideration is that constraints containing new variables be brought into the constraint set ....

....for j = 1 to jF j F j : F j ffl f return F The chief disadvantage of back substitution is the overhead to backtracking. Because we must be able to recapture earlier states of the solver, changes must either be trailed (e.g. 8, 4] or recovered by reversing the substitution operations (e.g. [6]) In particular, since column pointers are also maintained to ensure that we don t need to search for where back substitution should be applied, this information must also be recovered. 1.5 Partial Back Substitution Rather than performing full back substitution, it is possible for a CLP ....

P. Van Hentenryck and V. Ramachandran. Backtracking without Trailing in CLP(R Lin ). Proc. ACM-SIGPLAN Conference on Programming Language Design and Implementation. 349--360. 1994.

....of a unique slack variable with bounds [0; 0] to each equation. The basis for the validity of this operation is that one may substitute zero at any time for all such variables without changing the original problem statement. We call this special sort of slack variables witness variables after [6] where the very same trick was applied for a completely different purpose. The initial coefficients for the witness variables is immaterial, but 1 is convenient. As the solved form is manipulated, the coefficients change, and the witness variables track the dependencies between the constraints ....

.... there are (implicitly) fixed values and or additional equations, the extra cost for carrying along the witness variables is rewarded by the possibilities a) to deactivate the constraints later, and b) although not elaborated on here, to have backtracking without trailing in the constraint solver [6]. Our work shares objectives with [3] Our improvement is in the addition of defeasibility to the thread and that we don t need an explicit inverse of the basis for CS computations. With respect to applications we naturally envision classical dependency directed backtracking applications, but ....

Hentenryck P.van, Ranachandran V.: Backtracking without Trailing in CLP(R), Dept.of Computer Science, Brown University, CS-93-51, 1993.

....have been given a constant interest of researchers. From the recent works, Chakrabarti [6] proposed an algorithm which employs a marking technique similar to ours; however, he uses it to mark the current best solution. In the context of constraint logic programming, van Hentenryck and Ramachandran [18] proposed a new scheme called semantic backtracking. Again, the idea of using additional semantic information, which is mainly of heuristic nature, is similar to ours. The choice of Prolog as an implementation language has been justified by our experience. In fact, we should not speak about ....

P. van Hentenryck and V. Ramachandran. Backtracking without trailing in CLP(! Lin ). ACM Trans. on Programming Languages and Systems, 17(4):635--671, 1995.

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