Find an Affinity Problem

 

I - Equivalent (Alternative) Solutions:Is there more than one solution to a problem? Are there "equivalent algorithms" for solving a particular problem? What is the difference between an "equivalent solution" and "equivalent algorithm"?

Two algorithms are equivalent when they describe the SAME methodology, whereas equivalent solutions are based on getting the same result irrespective of the method.

Example 1: Sorting - there are many methods of sorting each of which provides the same answer for a given set of inputs, but some are better than others! Affinity solutions are important in exploring for a most efficient method.

Example 2: The first, obvious, solution to a problem may not always be the easiest or best solution. Even famous people such as Albert Einstein or John von Neumann did not always find the easiest alternative solutions to given problems. Review von Neumann's solution to the "Fly and Trains" problem.

More Examples:

I need to join two pieces of wood together:

Equivalent solutions:
  • Glue
  • Nails
  • Screws

I need to get from New York to Washington DC:

Equivalent solutions:
  • Drive a car
  • Catch a train
  • Fly a plane

II - Equivalent Problems: Can a problem in one area be equivalent to an already solved problem in another area?

The Human Genome problem may have solutions in Syntactic Analysis or Code Breaking

The "Four color problem": [Theorem] If a plane is divided into connected regions that are to be colored so that no two adjacent regions have the same color, it is never necessary to use more than four colors.

Solutions to Jigsaw problems are also found in Syntactic Analysis

 

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Last updated 2002/05/31
© J.A.N. Lee, 2000-2002.