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...e table with value a for x. The space complexity of the data structure is O(r · d · t). This space usage can be reduced by using a data structure called hologram [13]. Another index type, proposed in =-=[7]-=-, indexes, for each tuple and variable, the next tuple having a different value for the variable. Compression-based propagators compress the table in a form that allows a fast traversal. One of such c...

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...onstraints. The algorithms we give herein generate GAC propagators for arbitrary constraints that run in time O(nd), in extreme cases an exponential factor faster than any table constraint propagator =-=[4, 12, 7, 6, 17, 15]-=-. As our experiments show, generated propagators can even outperform hand-optimized propagators when performing the same propagation. Our approach is general but in practice does not scale to large co...

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...cal boundaries because the memory space required to represent them may grow exponentially with their arity. To reduce space complexity, researchers have focused on various forms of compression. Tries =-=[6]-=-, Multi-valued Decision Diagrams (MDDs) [3] and Deterministic Finite Automata (DFA) [22]are general structures used to represent table constraints in a compact way, so as to facilitate the filtering ...

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...ent is a crucial factor determining a Constraint Programming system speed, especially when d is too big. Gent et al. have recently described data structures used to propagate the constraints of a CSP =-=[3]-=-. To the best of our knowledge, the representation of a domain itself has not yet been the primary sector of interest of a specific publication in the area. Nevertheless, Schulte and Carlsson in their...

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...NAC4) with other AC algorithms, experimental evaluation on other benchmarks, including non-binary CSP instances and extension of NAC4 to handle negative tables represented in a compact way such as in =-=[12,13,14]-=-. Acknowledgment Many thanks to Jean-Noël Monette for his help in the experimental setting. This research is partially supported by the Interuniversity Attraction Poles Programme (Belgian State, Belgi...

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...ery over concrete tuples that any DBMS can evaluate in linear time. It is thus vital that our techniques yield acceptable performance. Equations 7 and 8 bound x to [min{1, 2, 3, 4},max{1, 2, 3, 4}] = =-=[1, 4]-=- and y to [min{2, 4, 6, 8},max{2, 4, 6, 8}] = [2, 8]. Given the equality x = y, ILP propagation deduces that x, y ∈ [2, 4], since [2, 4] is the intersection of permissible ranges for x and y. The memb...

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... for each X in the scope of C and a in the domain of X are created. The contents of the table are index to location of the corresponding tuples in C. This can be considered a very crude form of tries =-=[9]-=-. For example, if scope(C)= (X,Y ,Z) and C = {(3,6,7), (0,1,4), (3,0,4)}. Then C(X, 0) = {2}, C(X, 3) = {1,3}, C(Y, 1) = {2}, C(Y, 0) = {3}, C(Y, 6) = {1}, C(Z, 4) = {2,3}, C(Z, 7) = {1}. – preprocess...

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...orthand name for “variable/value pair”. For example x = a is a varval consisting of a variable x and a value a ∈ dom(x). Assume an implementation of table where tuples are stored as an array of tries =-=[GJMN07]-=-, one per variable, so that all tuples involving a particular varval are readily accessible, as illustrated in Figure 3.4. Example 3.11. The trie at the top of Figure 3.4 represents a set of tuples al...

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... three schemes GACv, GACa and GACva described in [8]. We do believe that GACva is a representative state-ofthe-art algorithm for table constraints. Our own experience confirms the results reported in =-=[4]-=-: GACva and the trie approach are quite robust and close in terms of performance. Here, we only provide some results obtained for some series of Crossword puzzles. For each grid, there is a variable p...

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...n a configuration problem, or may encode users’ preferences, among other applications. The table constraint is usually propagated using GAC-Schema, an algorithm proposed in [1] and studied further in =-=[9, 8, 4]-=- among others. In this paper, we introduce a compression algorithm for table constraints. This algorithm attempts to capture the structure that may exist in a table but ⋆ NICTA is funded by the Austra...