Tsoro and Hungarian approaches: A hybrid algorithm for an assignment problem

Tsoro is a two-person game which is widely played in Southern African countries. The idea of the game is to optimize (maximize or minimize) the number of playing stones depending on the objective of the game. There are many versions of this game. In this paper, we describe briefly these games and give details of the Matabele version, as it has a winning strategy that can be modified and applied to solve an assignment problem. We have known that the Hungarian method of assignment always results in an optimal solution to an assignment problem, and its iterative attempts are such that it moves from one infeasible to another infeasible solution such that it is moving towards a feasible optimal solution, until it has found one. Although optimal solution is guaranteed, it may be accomplished in some cases after many iterations. An approach based on the Tsoro strategy gives a feasible solution, but does not guarantee that solution is optimal. Hence, the Tsoro feasible solution can be regarded as an upper bound on the assignment optimal solution and the Hungarian method solution as its lower bound. If the difference between these two bounds is not significant, Tsoro solution may be accepted as a good working solution. In this paper, we first describe the Tsoro game in general and its Matabele version in particular, and based on the Matabele version of Tsoro, we present an hybrid algorithm for an assignment problem.