A Block World Problem Based Sudoku Solver Luciana Abednego, Cecilia Nugraheni Abstract—There are many approaches proposed for solving Sudoku puzzles. One of them is by modelling the puzzles as block world problems. There have been three model for Sudoku solvers based on this approach. Each model expresses Sudoku solver as a parameterized multi agent systems. In this work, we propose a new model which is an improvement over the existing models. This paper presents the development of a Sudoku solver that implements all the proposed models. Some experiments have been conducted to determine the performance of each model. Keywords—Sudoku puzzle, Sudoku solver, block world problem, parameterized multi agent systems. I. I NTRODUCTION S UDOKU is a very popular puzzle game. The components of this puzzle are a board, which is a 9 × 9 cells, divided into nine 3 × 3 subblocks, and a set of numbers from 1 to 9. The objective of this puzzle is to fill in every cell of the board with a number from 1 to 9 such that every row, every column, and every sub-block contains each number exactly one. Fig. 1 is an example of Sudoku Puzzles and its solution. Fig. 1. An example of Sudoku puzzle and its solution. There are many approaches for solving Sudoku puzzles, such as integer programming [1], SAT [5], genetic algorithm [6], [2], simulated annealing [7], meta-heuristics [4], neural networks [8], [13], particle swarm optimization [9], [10], and many more. In [11] we proposed an approach for solving Sudoku which is by modeling the puzzles as block-world problems. A block-world problem consists of a number of boxes on the table with a particular arrangement and two robots. Initially, all the boxes are on the table and are arranged into a number of piles. The objective of this problem is to change this arrangement into a targeted arrangement. The robots are responsible for changing the arrangement. Each robot has a special capability. The first robot is only capable to take a box from a table and put it on another box, whereas Luciana Abednego and Cecilia Nugraheni are with the Informatics the second robot is capable to take a box from a top of a pile and put it on the table. It is assumed that every time only one robot that can make a move. An example of block world problem is given in Fig. 2. Fig. 2. An example of block world problem. By modifying some settings of block world problem we have shown that Sudoku puzzles can be regarded as an variant of block world problems. We presented three block world problem based Sudoku solver models. The first model is based on backtracking principle. The solution searching is done exhaustively over the problem state space. The searching process stops when a solution is found or when there is no more alternative solution can be found. The second and the third model are based on fixed point principle. The solution search process is divided into nine sub-processes P = {p 1 ,p 2 ,...,p 9 }. Each sub-process, p i , tries to seek an empty cell for putting number i regarding some certain conditions/rules. If there are no more numbers can be placed on the board, the searching process halts. In [11] we have made a manually analysis of the mod- els’ performance. By using a Sudoku puzzle, we run each model’s algorithm to determine its performance. In this work, continuing our previous work, we defined a new model and developed a Sudoku solver based on the models. We then use the solver to do some experiments. The objective of the experiments are to measure the performance of each model. The remainder of this paper is organized as follows. In briefly the implementation principle of Sudoku Solver. Section IV discusses the experimental results. Conclusions and future work are given in Section V. II. SUDOKU SOLVER MODELS For the sake of clarification, in this section we give a summary of the Sudoku solver modeling presented in [11]. The readers may consult [11] for more detailed explanation. Following [4], we define a Sudoku puzzle as follows : Definition 1 Given an n 2 × n 2 cells divided into n × n distinct subblocks, the aim of Sudoku puzzle is to fill each cell so that the following three criteria are met: Department, Parahyangan Catholic University, Bandung, Indonesia (e-mail: luciana,cheni@unpar.ac.id). Section II we review our proposed models. Section III explains World Academy of Science, Engineering and Technology International Journal of Computer and Information Engineering Vol:8, No:8, 2014 1425 International Scholarly and Scientific Research & Innovation 8(8) 2014 scholar.waset.org/1307-6892/9999168 International Science Index, Computer and Information Engineering Vol:8, No:8, 2014 waset.org/Publication/9999168