Schoolgirls, football fixtures and multidimensional visualization What is the link

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2. 2 Schoolgirls Around 1850, Reverend Kirkman posed the problem: Consider a small girls’ school with 8 girls Each Sunday they walk to church in pairs How can we arrange the pairs so that each week girls walk with a different companion?

3. 3 Schoolgirls Algorithm

4. 4 Multidimensional visualization Hyperslice (van Liere and van Wijk, 1993) is a novel way of visualizing multidimensional functions To visualize F(w, x, y, z) they suggest a matrix of 2D projections – in each projection we keep 2 variables fixed and allow 2 variables to vary – ie a 2D visualization problem Along diagonal, we have visualization of function of 1 variable – hence a graph Note redundancy

5. 5 Rearranging the pictures Can we use the Schoolgirls algorithm to rearrange the pictures? Look at sequence of rows, rather than matrix – each row has information from each variable

6. 6 What about 3D? In fact, the original Kirkman’s problem was triples of schoolgirls (15 girls in total) There are 7 known solutions – here is one

7. 7 Multidimensional Visualization Selan dos Santos developed a 3D extension of Hyperslice, called HyperGraph Here is a function of 4 variables….

8. 8 Multidimensional visualization .. And a function of 6 variables Research question: How can we best arrange these subspaces?

9. 9 Suggestions? Schoolgirls algorithm is one possibility, but its general solution is still an unsolved problem (solutions only for n = 9, 15, 21, ..) Selan experimented also with a building metaphor, in which subspaces are indexed by rooms, floors and corridors Any other ideas??