---------
Omissions
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- Although it wasn't mentioned in our paper, it would have been
useful to point out that Figure 11 is a Hasse diagram,
showing the partially ordered set (poset) of slices,
partially ordered by set inclusion.
If we add the empty set as a final node at the bottom of the diagram,
we then have a Hasse diagram of the lattice (a kind of poset) of slices
of the entire space.
Similar lattices have been previously described and depicted, for example,
in the data cubes literature (e.g. Stolte, Tang, Hanrahan,
"Multiscale Visualization Using Data Cubes",
Proceedings of IEEE Symposium on Information Visualization (InfoVis) 2002).
Although Hasse diagrams are well known for depicting posets,
as far as we know, our paper is the first to point
out the polyarchical structure in Figure 11.
For more information, see the definitions of "poset", "lattice",
and "Hasse diagram" in MathWorld http://mathworld.wolfram.com/
and in the Wikipedia http://en.wikipedia.org/wiki/Main_Page
- Section 5.3, on the 9th page of the paper, may seem to
imply that, within a multitree, any two trees may share
at most one subtree.
In fact, two trees in a multitree may share any number of subtrees.
For example, in the multitree shown in Figure 1,
the two trees rooted at nodes A and C, respectively,
share two subtrees, rooted at nodes F and P, respectively.
- A copy of Giampaolo's book (reference 10) is at
http://www.nobius.org/~dbg/practical-file-system-design.pdf
- An interesting visualization of mSpace:
Paulo Pacheco and m. c. schraefel
Focus + Context + Orientation with the Phaser Tool
Poster Proceedings of ACM Symposium
on User Interface Software and Technology (UIST) 2002
2 pages
http://www.dgp.utoronto.ca/~ppacheco/Publications.htm
- George W. Furnas' CHI 1997 paper "Effective View Navigation"
gives balanced trees and hypercubes as two examples (on the 3rd page)
of Efficiently View Traversable (EVT) structures.
It's interesting to consider the mSpace polyarchy for such
a hypercube, and realize that each of the trees in the
mSpace polyarchy is a balanced tree and is also EVT.
This helps explain how balanced trees and hypercubes are
both EVT: when specifying the coordinates of an element
in the hypercube, one coordinate at a time,
this corresponds to travelling down a tree,
one level at a time, choosing a branch at each step.
- Jacques Bertin's book
@book{bertin1967,
author={Jacques Bertin},
title={S\'{e}miologie graphique:
Les diagrammes, Les r\'{e}seaux, Les cartes},
year=1967,
publisher={\'{E}ditions Gauthier-Villars},
address={Paris},
note={(2nd edition 1973, English translation 1983)}
}
contains a picture of a polyarchy (page 283 of the 2nd edition)
which shows 2 trees of an mSpace polyarchy.
There are 3 attributes, each with 3 possible values:
species (seal, bear, eagle), individual (1, 2, 3),
and body part (head, neck, feet).
The 27 leaf nodes are shared between both trees,
each of which has 3 levels, with each level corresponding to one attribute.
Each of the 2 trees involves a different ordering of attributes.
-----------------------
Additional Related Work
-----------------------
- related to zzstructures:
Theodor Holm Nelson
A Cosmology for a Different Computer Universe:
Data Model, Mechanisms, Virtual Machine and Visualization Infrastructure
Journal of Digital Information, Volume 5 Issue 1
Article No. 298, 2004-07-16
http://jodi.ecs.soton.ac.uk/Articles/v05/i01/Nelson/
http://jodi.ecs.soton.ac.uk/Articles/v05/i01/Nelson/?printable=1
Jan Theodore Galkowski
Notes on an interpretation of Nelson's zzstructure
29th October 2004
http://algebraist.com/
- multidimensional space combined with multitrees:
Hartmut Obendorf, Sven Bertel, Kai-Florian Richter
Supporting User-Specific Views Via Multidimensional Trees
CHI 2001 poster
http://doi.acm.org/10.1145/634067.634310
- work that makes use of an ordering of dimensions:
% Hierarchical Axis
@inproceedings{mihalisin1991b,
author = {Ted Mihalisin and John Timlin and John Schwegler},
title = {Visualization and Analysis of Multi-variate Data:
A Technique for all Fields.},
booktitle = {Proceedings of IEEE Visualization},
year = 1991,
pages = {171--178}
}
@inproceedings{yang2003,
author = {Jing Yang and Wei Peng and Matthew O. Ward
and Elke A. Rundensteiner},
title = {Interactive Hierarchical Dimension Ordering,
Spacing and Filtering for Exploration
of High Dimensional Datasets},
booktitle = {Proceedings of IEEE Symposium on
Information Visualization (InfoVis)},
year = 2003,
pages = {105--112}
}