Milan Banković

Milan Banković

In this paper, we present an approach to automated solving of triangle ruler-and-compass construction problems using finite-domain constraint solvers. The constraint model is described in the MiniZinc modeling language, and is based on the automated planning. The main benefit of using general constraint solvers for such purpose, instead of developing dedicated tools, is that we can rely on the efficient search that is already implemented within the solver, enabling us to focus on geometric aspects of the problem. We may also use the solver's built-in optimization capabilities to search for the shortest possible constructions. We evaluate our approach on 74 solvable problems from the Wernick's list, and compare it to the dedicated triangle construction solver ArgoTriCS. The results show that our approach is comparable to dedicated tools, while it requires much less effort to implement. Also, our model often finds shorter constructions, thanks to the optimization capabilities offered by the constraint solvers.

Milan Banković

In this paper, we investigate the possibility of improvement of the widely-used filtering algorithm for the linear constraints in constraint satisfaction problems in the presence of the alldifferent constraints. In many cases, the fact that the variables in a linear constraint are also constrained by some alldifferent constraints may help us to calculate stronger bounds of the variables, leading to a stronger constraint propagation. We propose an improved filtering algorithm that targets such cases. We provide a detailed description of the proposed algorithm and prove its correctness. We evaluate the approach on five different problems that involve combinations of the linear and the alldifferent constraints. We also compare our algorithm to other relevant approaches. The experimental results show a great potential of the proposed improvement.