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representing seating plan by student preference quandry

  • 23-01-2015 10:06am
    #1
    evolving_doors
    Closed Accounts Posts: 11,812 ✭✭✭✭


    Hi Folks,

    I have a class of 29 pupils and they have written down 3 people who they want to sit beside. What is the best way of representing this data on a chart/diagram... (Prefereably by entering the data into Excel or some online site). There is loads of other criteria such as grade scores and behaviour but I'll go with their requests first and see what a chart looks like

    I was thinking a spider/radar chart but maybe it would be too many lines.

    Any thoughts would be greatly appreciated. its not quite maths but maybe consider it in terms of attempting to ensure the probability that everyone gets to sit beside at least one person on their list... If it maters there are 8 groups of 2 tables and 2 groups of 4 tables and 1 group of 5 tables.

    xx   xxxx   xx
    xx   xxxxx xx
    xx   xxxx   xx
    xx             xx

    Edit: (This is honestly not an assignment)


Comments

  • #2
    MathsManiac
    Registered Users, Registered Users 2 Posts: 1,595 ✭✭✭MathsManiac


    Since you've no replies yet, I'll float a notion.

    This strikes me as a situation that could be represented as a directed graph with 29 nodes and three (directed) edges out of each node.

    Are the tables round? If so, you want a partition of the graph into cycles that match your table groupings or subsets thereof.

    For a start, if you don't have at least eight 2-cycles, you're snookered. (2-cycle in this case is a pair of people who each want to sit beside each other).

    If your tables aren't round, then cycles aren't quite what you want - instead it would be "chains" of undirected edges in which both ends are origins of a directed edge. Anyway, it's then a computer programming problem really!

    Is this of theoretical interest, or a practical problem you're trying to solve? If it's practical, I'd suggest you forget about trying to mathematise it. Get 29 cards, write each student's name on it, along with the three people they've nominated, and keep shuffling them around until the first of the following happens:
    • you get it to work
    • you give up
    • the school year ends and they all feck off for the holidays anyway.


  • #3
    ray giraffe
    Registered Users, Registered Users 2 Posts: 338 ✭✭ray giraffe


    Sounds like Maximum Common Edge Subgraph Problem


  • #4
    evolving_doors
    Closed Accounts Posts: 11,812 ✭✭✭✭evolving_doors


    Thanks folks , for a finish though I wrote all the names in a circle on A5 sheet and drew lines to each of the three preferences. It was a bit of a mess but I worked on the middle row first, I.e. most popular on the inside so two were either side. then the first and third row got at most one preference!.

    It would be an interesting software program if you could input other criteria (students with short sight, students with high grades to sit/not sit with each other, boldies up the front)


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