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Home / Proceedings / Proceedings of the AAAI Conference on Artificial Intelligence, 21

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

February 1, 2023

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Authors

Carlos Ansotegui

Ramon Bejar

Cesar Fernandez

Carla Gomes

Carles Mateu

DOI:


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 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 puzzle: 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.

Topics: AAAI

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Carlos Ansotegui|| Ramon Bejar|| Cesar Fernandez|| Carla Gomes|| Carles Mateu The Impact of Balancing on Problem Hardness in a Highly Structured Domain Proceedings of the AAAI Conference on Artificial Intelligence, 21 (2006) 10.

Carlos Ansotegui|| Ramon Bejar|| Cesar Fernandez|| Carla Gomes|| Carles Mateu The Impact of Balancing on Problem Hardness in a Highly Structured Domain AAAI 2006, 10.

Carlos Ansotegui|| Ramon Bejar|| Cesar Fernandez|| Carla Gomes|| Carles Mateu (2006). The Impact of Balancing on Problem Hardness in a Highly Structured Domain. Proceedings of the AAAI Conference on Artificial Intelligence, 21, 10.

Carlos Ansotegui|| Ramon Bejar|| Cesar Fernandez|| Carla Gomes|| Carles Mateu. The Impact of Balancing on Problem Hardness in a Highly Structured Domain. Proceedings of the AAAI Conference on Artificial Intelligence, 21 2006 p.10.

Carlos Ansotegui|| Ramon Bejar|| Cesar Fernandez|| Carla Gomes|| Carles Mateu. 2006. The Impact of Balancing on Problem Hardness in a Highly Structured Domain. "Proceedings of the AAAI Conference on Artificial Intelligence, 21". 10.

Carlos Ansotegui|| Ramon Bejar|| Cesar Fernandez|| Carla Gomes|| Carles Mateu. (2006) "The Impact of Balancing on Problem Hardness in a Highly Structured Domain", Proceedings of the AAAI Conference on Artificial Intelligence, 21, p.10

Carlos Ansotegui|| Ramon Bejar|| Cesar Fernandez|| Carla Gomes|| Carles Mateu, "The Impact of Balancing on Problem Hardness in a Highly Structured Domain", AAAI, p.10, 2006.

Carlos Ansotegui|| Ramon Bejar|| Cesar Fernandez|| Carla Gomes|| Carles Mateu. "The Impact of Balancing on Problem Hardness in a Highly Structured Domain". Proceedings of the AAAI Conference on Artificial Intelligence, 21, 2006, p.10.

Carlos Ansotegui|| Ramon Bejar|| Cesar Fernandez|| Carla Gomes|| Carles Mateu. "The Impact of Balancing on Problem Hardness in a Highly Structured Domain". Proceedings of the AAAI Conference on Artificial Intelligence, 21, (2006): 10.

Carlos Ansotegui|| Ramon Bejar|| Cesar Fernandez|| Carla Gomes|| Carles Mateu. The Impact of Balancing on Problem Hardness in a Highly Structured Domain. AAAI[Internet]. 2006[cited 2023]; 10.


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