Conference Paper

The Impact of Balancing on Problem Hardness in a Highly Structured Domain.

Conference: Proceedings, The Twenty-First National Conference on Artificial Intelligence and the Eighteenth Innovative Applications of Artificial Intelligence Conference, July 16-20, 2006, Boston, Massachusetts, USA
Source: DBLP

ABSTRACT Random problem distributions have played a key role in the study and design of algorithms for constraint sat- isfaction and Boolean satisfiability, as well as in our understanding 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 re- gions 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 consider- ably harder than QCP/QWH instances of the same size. More interestingly, we show the impact of different bal- ancing 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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