Sorting Networks

To make computers go faster, it can be a lot more effective to have several slower computers working on a problem than a single fast one. This raises questions about how much of the computation can be done at the same time.

Here we use a fun team activity to demonstrate an approach to parallel sorting. It can be done on paper, but we like to get students to do it on a large scale, running from node to node in the network.

 

Extensions:

  • As an extra challenge for the children, have them do the activity completely silently
  • Use words (compared using dictionary order) instead of numbers for sorting. This will generally slow the children down, especially if some words start with the same letters
  • This is a good exercise for thinking about permutations. For example, with 6 people entering the sorting network, there are 6x5x4x3x2x1=720 possible orders that they can start in, yet only one way that they will come out. When children are designing their own sorting networks, they should test them with all possibly input patterns. For example, to check a 3-input sorting network, there are 6 (3x2x1) possible input permutations, and for 4 inputs there are 24 (4x3x2x1) permutations, and for n inputs there are n! (factorial) permutations. These numbers get larger very rapidly
  • Jeff Gray from University of Alabama at Birmingham has the following suggestion as an extension to this activity using robotics:
    • Place the robots on an initial position in a sorting network.
    • Have each robot generate a random number
    • Have the robots do the pairwise comparison thorugh Bluetooth using unique identifiers of each robot
    • Coordination of “Traffic” will be needed so the robots can move across the network so that they do not bump into each other.

Activity description (PDF)

Videos

  • Jeff Gray from University of Alabama at Birmingham has the following suggestion as an extension to this activity using robotics:
    • Place the robots on an initial position in a sorting network.
    • Have each robot generate a random number
    • Have the robots do the pairwise comparison thorugh Bluetooth using unique identifiers of each robot
    • Coordination of “Traffic” will be needed so the robots can move across the network so that they do not bump into each other.

Photos

  • Photos from Computer Science camps for students aged 8-12, run by Mark Laprairie of the University of Regina.