We describe an online, interactive system with a graphical interface to illustrate the power and operation of consistency algorithms in a friendly and popular context, namely, solving Sudoku puzzles. Our tool implements algorithms for enforcing five (domain-based) consistency properties on binary and non-binary constraint models. Our tool is useful for research, education, and outreach. From a scientific standpoint, we propose a new consistency property that can solve the hardest known 9×9 Sudoku instances without search, but leave open the question of the lowest level of consistency needed to solve every 9×9 Sudoku puzzle. We have used the current tool in the classroom to introduce students to modeling problems with constraints, explain consistency properties, and illustrate the operations of constraint propagation and lookahead. Finally, we have also used this tool during outreach activities to demystify AI to children and the general public and show them how computers 'think.'
In this paper, we argue that metrics that assess the performance of backtrack search for solving a Constraint Satisfaction Problem should not be visualized and examined only at the end of search, but their evolution should be tracked throughout the search process in order to provide a more complete picture of the behavior of search. We describe a process that organizes search history by automatically recognizing qualitatively significant changes in the metrics that assess search performance. To this end, we introduce a criterion for quantifying change between two time instants and a summarization technique for organizing the history of search at controllable levels of abstraction. We validate our approach in the context of two algorithms for enforcing consistency: one that is activated by a surge of backtracking and the second that modifies the structure of the constraint graph. We also introduce a new visualization for exposing the behavior of variable ordering heuristics and validate its usefulness both as a standalone tool and when displayed alongside search history.
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