The impact of balancing on problem hardness in a highly structured domain
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Date
2006
Authors
Ansótegui Gil, Carlos José
Béjar Torres, Ramón
Fernàndez Camon, César
Gomes, Carla
Mateu Piñol, Carles
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Abstract
Random problem distributions have played a key role in the study and design of algorithms for constraint satisfaction and Boolean satisfiability, as well as in ourunderstanding of problem hardness, beyond standard worst-case complexity. We consider random problem
distributions from a highly structured problem domain that generalizes the Quasigroup Completion problem (QCP) and Quasigroup with Holes (QWH), a widely used domain that captures the structure underlying a range of real-world applications. Our problem domain is also a generalization of the well-known Sudoku puz-
zle: we consider Sudoku instances of arbitrary order, with the additional generalization that the block regions can have rectangular shape, in addition to the standard square shape. We evaluate the computational hardness of Generalized Sudoku instances, for different
parameter settings. Our experimental hardness results show that we can generate instances that are considerably harder than QCP/QWH instances of the same size. More interestingly, we show the impact of different balancing strategies on problem hardness. We also provide
insights into backbone variables in Generalized Sudoku instances and how they correlate to problem hardness.
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Proceedings of the twenty-first National Conference on Artificial Intelligence, 2006, p. 10-15