Exploring Properties of Icosoku by Constraint Satisfaction Approach

Icosoku is a challenging and interesting puzzle that exhibits highly symmetrical and combinatorial nature. In this paper, we pose the questions derived from the puzzle, but with more difficulty and generality. In addition, we also present a constraint programming model for the proposed questions, which can provide the answers to our first two questions. The purpose of this paper is to share our preliminary result and problems to encourage researchers in both group theory and constraint communities to consider this topic further.

The Regularization of Small Sub-Constraint Satisfaction Problems

This paper describes a new approach on optimization of constraint satisfaction problems (CSPs) by means of substituting sub-CSPs with locally consistent regular membership constraints. The purpose of this approach is to reduce the number of fails in the resolution process, to improve the inferences made during search by the constraint solver by strengthening constraint propagation, and to maintain the level of propagation while reducing the cost of propagating the constraints. Our experimental results show improvements in terms of the resolution speed compared to the original CSPs and a competitiveness to the recent tabulation approach. Besides, our approach can be realized in a preprocessing step, and therefore wouldn't collide with redundancy constraints or parallel computing if implemented.