Branch and Bound Case Studies
Explore core optimization problems and the mechanics of state space pruning.
Solving the classic binary selection problem using branch-and-bound to prune infeasible subtrees, ensuring maximum profit within weight constraints.
Branching Depth
O(2^n)
Pruning Rate
High
Complexity
NP-Hard
Bound Method
Fractional
Minimizing total tour cost for a salesman visiting cities exactly once. Uses reduced cost matrices to establish lower bounds for pruning.
Tour Cost
Minimal
Matrix Redux
Row/Col
Bound Type
Lower
Search Type
Best-First
Visualizing the hierarchical expansion of nodes. Demonstrates how bounding functions eliminate suboptimal branches early in the search.
Node Status
Active
Pruning Logic
c(x) > U
Queue Type
FIFO/LIFO
Efficiency
Optimal
Need a deep dive into optimization theory?
We provide comprehensive lecture materials, state space tree visualizations, and step-by-step bounding derivations.
Method Comparison
Compare Branch and Bound against standard paradigms. Analyze efficiency, memory usage, and pruning capabilities for NP-hard problems.
| Method | Complexity | Speed | Outcome |
|---|---|---|---|
DP Dynamic | High (O(n^2)) | Fixed | Optimal |
BACK Search | High (Exp) | Variable | Exhaustive |
B&B Optimal | Adaptive | Optimized | Pruned |
GRDY Heuristic | Low (O(n)) | Minimal | Local |
BRUTE Naive | Max (O(n!)) | Infinite | Full |
Efficiency
Branch and Bound prunes search space effectively.
Memory
Requires heap space for the priority queue.
Speed
Faster than brute force for large datasets.