Assignment Problem(2) - State Space Tree

 Sample Assignment Problem





State Space Tree

The root node represents the starting point where no assignments have been made yet.

Each branch from the root represents a possible job assignment for Worker 1 (denoted as x1).

The second level represents possible assignments for Worker 2 (denoted as x2), given the job already assigned to Worker 1.

In a full state space tree, this process would continue for Workers 3 and 4, each with their own level in the tree, until all workers are assigned jobs without conflict, resulting in a complete solution at the leaf nodes.


Full state Space Tree


Each path from the root to a leaf node represents a complete set of job assignments, one for each worker. There are 4! = 24 possible paths, each corresponding to a different way to assign all four jobs to the four workers without any overlaps. ​


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