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.

  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: We present a new probabilistic framework for finding likely variable assignments in difficult constraint satisfaction problems. Finding such assignments is key to efficient search, but prac-tical efforts have largely been limited to random guessing and heuristically designed weighting systems. In contrast, we derive a new version of Belief Propagation (BP) using the method of Ex-pectation Maximization (EM). This allows us to differentiate between variables that are strongly biased toward particular values and those that are largely extraneous. Using EM also eliminates the threat of nonconvergence associated with regu-lar BP. Theoretically, the derivation exhibits ap-pealing primal/dual semantics. Empirically, it produces an "EMBP"-based heuristic that out-performs existing techniques for guiding variable and value ordering during backtracking search.
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: In this paper we describe models of the logic puzzle Kakuro as a constraint problem with finite domain variables. We show a basic model expressing the constraints of the problem and present various im-provements to enhance the constraint propagation, and compare alterna-tives using MILP and SAT solvers. Results for different puzzle collections are given. We also propose a grading scheme predicting the difficulty of a puzzle for a human and show how problems can be tightened by removing hints.
  • [Show abstract] [Hide abstract]
    ABSTRACT: The sudoku completion problem is a special case of the latin square completion problem and both problems are known to be NP-complete. However, in the case of a rectangular hole pattern–i.e. each column (or row) is either full or empty of symbols–it is known that the latin square completion problem can be solved in polynomial time. Conversely, we prove in this paper that the same rectangular hole pattern still leaves the sudoku completion problem NP-complete.
    Discrete Mathematics 11/2012; 312(22-22):3306-3315. DOI:10.1016/j.disc.2012.07.022 · 0.57 Impact Factor

Full-text (2 Sources)

Available from
May 23, 2014