Solving Knights Covering Problem by a Hybrid Algorithm

Abstract

There are problems which do not have analytical solutions and require algorithms (such as Backtracking) that use brute force. The time complexity of these algorithms is polynomial, so they lose their practical advantage for even small systems. In this study, we apply the hybrid algorithm to find the number of knights required to cover every square of a chessboard-looking table (a.k.a. Knights Covering Problem) to reduce time complexity. This approach simplifies the problem by removing the attacked cells in order to decrease the number of trial-and-error steps. The hybrid algorithm increases efficiency by reducing computation time. Our analysis shows 50% performance increment for 4-KCP.