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CS 312: Algorithm AnalysisPowerPoint Presentation

CS 312: Algorithm Analysis

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### CS 312: Algorithm Analysis

This work is licensed under a Creative Commons Attribution-Share Alike 3.0 Unported License.

Lecture #39: Problem Solving

Credit: Eric Ringger

A Rough-Draft Set of Questionsfor Problem Solving

Problem-Solving

- Problem Formulation
- Algorithm Design
- Algorithm Analysis
- Theoretical Analysis: classify as asymptotic order of growth
- Empirical Analysis
- Proofs of Correctness

Questions for Problem Formulation

- What do I know?
- What do I not know but I want to know?
- What are my assumptions?
- Can I formulate the problem as a graph?
- Can the problem be reduced to a familiar problem?
- Is the problem an optimization problem?
- Is the objective linear?

- Does the problem have constraints?
- Are the constraints linear?

Questions for Algorithm Design

- Do I recognize the problem and know an algorithm that solves this problem?
- Is the problem NP-Hard but not NP-Complete?
- Is the problem NP-complete?
- Is it in NP?
- Can I reduce a known NP-complete problem to it?

- Does the problem decompose nicely into sub-problems?
- Do the sub-problems overlap?
- Does the optimality property hold?

Exercise

- Can you organize these questions (both problem formulation and algorithm design) into a usable decision tree to guide you in the practice of problem-solving?

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