Information Theory Perspective on Graph Search

Core Principle

DFS maximizes information gain per step by fully exploring each branch (greedy for path information), while BFS maintains maximum entropy by keeping all options open at each level.

Why This Matters

This information-theoretic view explains why different search strategies are optimal for different problem types. It connects algorithmic choices to fundamental principles about uncertainty, knowledge acquisition, and decision-making under incomplete information.

Evidence/Examples

• DFS commits to paths early → high information gain but potential for local optima
• BFS maintains uncertainty longer → guaranteed global optimum in unweighted cases
• Each BFS level represents an isodistance set (equal information content)
• DFS backtracking represents information “unlearning” when paths fail

Implications

• Exploration vs. exploitation trade-off: DFS exploits early information, BFS explores broadly
• Risk management: BFS hedges against making wrong early commitments
• Resource allocation: DFS concentrates resources, BFS distributes them
• Learning strategies: deep specialization vs. broad foundation

Related Ideas

• DFS vs BFS - Fundamental Exploration Dichotomy
• Graph Algorithms Optimal Complexity
• Optimal Stopping Theory
• Entropy and Decision Making

Questions

• How do these information principles apply to human learning and career decisions?
• What’s the mathematical relationship between search strategy and information entropy reduction?
• Can we quantify the information content of different search strategies?