Randomised Analysis of Backtracking-based Search Algorithms in Elucidating Sudoku Puzzles Using a Dual Serial/Parallel Approach

Sudoku is a 9x9 grid-based puzzle. It is a game where each row, column, and 3x3 box must have one instance of a number from 1 to 9. In present paper, we shall evaluate three different algorithmic approaches both in serial and parallel configurations that can be utilised to solve a puzzle of Sudoku to assess their comparative performance metrics for differential randomly generated Sudoku datasets. We shall utilise Breadth-first search, Depth-first search, Depth-first search with Breadth-first search parallelisation for sub-tress, for evaluating a large number of randomly generated Sudoku puzzles with a varying number of clues to find the best algorithm based on time and space complexity as well as clue complexity. With this, we shall analyse and develop a best practice algorithm that can be ideally used to solve a large number of puzzles in any given situation in the most time-efficient manner. Our analysis has found that there was a significant improvement in utilising the parallel algorithm over both the Breadth-first and Depth-first search approaches from 28% to over 56%. Even moving from Breadth-first to Depth-first search, we have gauged quite a moderate improvement in performance from 15 to 21%.