Lines Matching defs:with
6 % in compliance with the License. You may obtain a copy of the License
43 (in this context, we only consider domains with a finite number of values).
61 with the problem size:
79 Figure \ref{figsearchspace} shows a search space with N (here 16)
103 Here is a selection of search methods together with their properties:
125 partitioning it systematically. This can be done naturally with a
130 completely (with as little as O(N) memory requirements).
166 is only possible with constructive methods which allow one to reason about
170 This can only be implemented with
218 Since search space sizes grow exponentially with problem size,
225 This can be done with the help of constraints. This is often referred
245 \section{Complete Tree Search with Heuristics}
257 into play here because we deal with finite search trees.
343 While with 2 variables there are only 2 variable selection strategies,
344 this number grows exponentially with the number of variables. For 5
351 down, variables with small domains should be selected first.
410 We model the problem with one variable per queen, assuming that each queen
437 We start naively, using the pre-defined labeling-predicate that comes with the
456 variables with the smallest domain first. This reduces the branching
471 the first solution is found with only 3 backtracks now.
473 nicely with the naive strategy, but our improvement leads to a
475 This is not uncommmon with heuristics: one has to keep in mind that the
477 results with some problems can be useless or counter-productive with others.
533 It allows us to specify that we want to start labeling with the middle value
547 performance has become more predictable than with the
564 \caption{N-Queens with different labeling strategies: Number of backtracks}
627 \item With a perfect heuristic, the first solution is found with zero
713 side of the search tree. This often makes sense because with a good
717 tree with 5 binary variables).
726 tree. In many constraint problems with a fixed number of variables
731 depth-bounded search with bounded-backtrack search. The following
738 \caption{Depth-bounded, combined with bounded-backtrack search}
775 starting the search at the tree root with a certain integral amount of
778 be split any further: subtrees provided with only a single credit unit
817 The number of leaf nodes grows exponentially with the number of
826 is not good enough. A possible remedy is to combine credit search with
841 In this implementation, credit search is always combined with another
845 of solutions, but these solutions are not the leftmost ones (like with
860 bounded backtrack search with a limit of 0 backtracks.
897 the heuristic. LDS starts searching with a discrepancy of $0$ (which
899 a solution with a given discrepancy, the discrepancy is increased and
903 to apply LDS with small discrepancies. Subsequently, if no solution
915 value selection choice as the heuristically best value with
922 \caption{Incomplete search with LDS}
942 The reference also suggests that combining LDS with Bounded Backtrack
944 accordingly supports the combination of LDS with BBS and DBS.
968 %{\eclipse} installation. You can copy this file and load it with
1031 %cope with this we use the {\eclipse} ``tentative value'' facility in
1033 %The heuristic is stored with the variable as its tentative value.
1172 between 1 and some upper bound Max (start with, say Max = $N^2$),