Automatic Synthesis of Smart Table Constraints by Abstraction of Table Constraints

The smart table constraint represents a powerful modeling tool that has been recently introduced. This constraint allows the user to represent compactly a number of well-known (global) constraints and more generally any arbitrarily structured constraints, especially when disjunction is at stake. In many problems, some constraints are given under the basic and simple form of tables explicitly listing the allowed combinations of values. In this paper, we propose an algorithm to convert automatically any (ordinary) table into a compact smart table. Its theoretical time complexity is shown to be quadratic in the size of the input table. Experimental results demonstrate its compression efficiency on many constraint cases while showing its reasonable execution time. It is then shown that using filtering algorithms on the resulting smart table is more efficient than using state-of-the-art filtering algorithms on the initial table.