The space complexity of a search algorithm refers to the amount of memory required to execute the algorithm. In the case of greedy search, the space complexity can be determined by considering the number of nodes that need to be stored in memory during the search process.

The space complexity of greedy search can be analyzed by considering two factors: the branching factor (b) and the maximum depth of the search tree (m).

- **Branching Factor (b):** The branching factor represents the maximum number of child nodes that can be generated from a single node in the search tree. In other words, it determines the number of possible choices or actions available at each level of the search tree.

- **Maximum Depth of the Search Tree (m):** The maximum depth of the search tree represents the length of the longest path from the root node to any leaf node in the tree. It determines the maximum number of levels or steps required to reach a solution.

The space complexity of greedy search can be determined by considering the maximum number of nodes that need to be stored in memory at any given time during the search process.

- At each level of the search tree, the number of nodes can be at most equal to the branching factor raised to the power of the level. So, at level 1, there can be at most b^1 nodes, at level 2 there can be at most b^2 nodes, and so on.

- Since the maximum depth of the search tree is m, the total number of nodes in the search tree can be at most b^m.

Therefore, the space complexity of greedy search is given by O(b^m), where O represents the upper bound or worst-case scenario.

Hence, the correct option is (c) O(b^m)