🔀 Problem Decomposition & AO*

1. 🎯 Learning Objectives

• Represent problems as AND-OR graphs
• Trace AO* on a small AND-OR tree
• Explain the difference between AND nodes and OR nodes
• Apply problem decomposition strategies

2. 📖 Core Content

3.1 AND-OR Graphs

• OR nodes: Any one child solves the problem (alternatives)
• AND nodes: All children must be solved (subproblems)

3.2 AO* Algorithm

text
AOStar(root):
    while root not SOLVED:
        // Find best partial solution graph
        G = find_best_partial(root)
        // Expand tip nodes
        for tip in G.tips():
            expand(tip)
            compute new heuristic values
        // Propagate cost updates upward
        propagate_costs(root)

3.3 Node Value Calculation

• OR node: $f(n) = \min_{c \in children} f(c)$
• AND node: $f(n) = \sum_{c \in children} f(c)$ (or max, depending on definition)

4. 📝 Practice Questions

Q1: In an AND-OR tree, if an AND node has children with values [3, 5, 2], what is the node's value?

Answer: For an AND node using sum, value = 3+5+2 = 10. For an AND node using max (parallel tasks), value = max(3,5,2) = 5. The interpretation depends on problem semantics. Join Discord PreviousBlocks WorldNextGraphplan & PSP