CS 411 Fall 2025  >  Outline for December 1, 2025

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CS 411 Fall 2025
Outline
for December 1, 2025

Outline

Coping with the Limitations of Algorithmic Power [L Ch 12 intro]

• Idea 1: Solve something else
  • Solve a special case.
  • Approximate a solution.
  • Optimization: find a feasible solution that is good enough, although it may not be optimal.
• Idea 2: Prune the state-space tree
  • See Backtracking.

Backtracking [L 12.1]

• Many algorithms go through a state space in a DFS-like manner. Partial solutions are gradually built into (full) solutions. In an exhaustive search, we traverse the entire state space.
• Backtracking
  • A partial solution is promising if it might lead to a full solution.
  • Backtrack immediately if not promising.
  • Backtracking means we skip some branches of the state-space tree; we prune the tree.
  • Example: \(n\)-Queens problem.
  • Backtracking is generally not a method for producing fast algorithms, although it does often result in faster algorithms.