Multidimensional appropriate clustering and DBSCAN for SAT solving

This paper is an extended version of Hireche and Drias (2018) presented at the WORLD-CIST’18 conference. The major contribution, in this work, is defined in two phases. First of all, the use of data mining technologies and especially the tools of data preprocessing for instances of hard and complex problems prior to their resolution. The authors focus on clustering the instance aiming at reducing its complexity. The second phase is to solve the instance using the knowledge acquired in the first step and problem-solving methods. The paper aims to discuss these issues.

Because different clustering techniques may offer different results for a data set, a prior knowledge on data helps to determine the adequate type of clustering that should be applied. The first part of this work deals with a study on data descriptive characteristics in order to better understand the data. The dispersion and distribution of the variables in the problem instances is especially explored to determine the most suitable clustering technique to apply.

Several experiments were performed on different kinds of instances and different kinds of data distribution. The obtained results show the importance and the efficiency of the proposed appropriate preprocessing approaches prior to problem solving.

The proposed approach is developed, in this paper, on the Boolean satisfiability problem because of its well-recognised importance, with the aim of complexity reduction which allows an easier resolution of the later problem and particularly an important time saving.

State of the art of problem solving describes plenty of algorithms and solvers of hard problems that are still a challenge because of their complexity. The originality of this work lies on the investigation of appropriate preprocessing techniques to tackle and overcome this complexity prior to the resolution which becomes easier with an important time saving.