17

Tractable and Non-Tractable Problems

Objectives

After reading this chapter, you should understand:

  • The need for problem classification: Tractable and Intractable
  • Upper and Lower Bounds
  • Algorithmic Gap: Why the Lower Bound of a Problem and the Best Case of an Algorithm are Different
  • The Class NP-Complete: Why it is a closed set
  • Problem Transformation: One NP-complete problem to another
  • NP-Completeness: How is it proved and Problem Reduction
  • Non-Deterministic Algorithms
  • The most famous open problem in Computer Science: P = NP ?
  • Cook’s Theorem: First known proof of NPCompleteness
  • Approximate Solutions – What it is about
  • The complexity Classes and the meaning of Intractability
  • Undecidable and Non-Computable problems
  • The Halting Problem ...

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