Databases and Systems

which minimizes dispersion. The optimization problem is linear and has a small
number of variables, so it should be easily solvable.
Map Integration
y = 4.433*x + -177.1 ; r=0.97
Figure 8: Direct minimization of dispersion
Another approach to the query problem is to integrate the maps, and use coordinates
in the integrated map as universal coordinates for querying purposes. What does
integration mean? Don't the universal coordinate procedures described above
perform a sort of integration, by placing all the elements of all the maps in a common
framework? Yes and no. The universal coordinate approach can be viewed as
producing a universal map which has one element for each map element in each of
the source maps. A marker that appears in several maps will be associated with
multiple map elements in such a universal map. An integrated map, by contrast,
would put every marker in just one position, no mater how many primary maps it
occurred in. That position should have an associated window of uncertainty, and
should be influenced by the marker's positions in the different source maps. The
uncertainty should be truly reflective of the available information on the marker's
position. Integration should ideally also eliminate the need to arbitrarily select one
map as a standard, which introduces biases. The coordinates and uncertainties
resulting from a meaningful integration along these lines might yield significantly
improved query behavior over universal coordinates. See [4,5] for work in this area.
Unfortunately, meangful integrated maps are considerably more difficult to construct
than alignments; a key issue is how to combine order data from multiple maps and
preserve it in the integrated map. There are also a number of technical difficulties
associated with defining a meaningful notion of an uncertainty window for a locus on
an integrated map. Mapping uncertainty is normally associated with pairwise
distances, yet for a map to be efficiently searchable it must use coordinates rather
than intermarker distances. The standard error of a coordinate assignment as not a
well defined concept, and yet some such notion is necessary to implement an
appropriately fuzzy search. This is an important area for future work that affects the
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