The building blocks of a graphical presentation are the techniques for identifying a single element from a set of possible values. Several characteristics of a set are relevant to choosing an appropriate graphical technique. One characteristic is determining ordering relationships as quantitative, ordinal, or nominal. Another identifies whether an element is a coordinate (e.g., temporal, such as calendar date; or spatial, such as latitude) or an amount (e.g., number of days or weight). A third determines if sets can belong to the different domains of time, space, temperature, or mass. This information helps to preserve subtle stylistic conventions, such as using a horizontal axis for time coordinates and a vertical axis for temperature. These characterizations can also be helpful for judging how to group and integrate relations within pictures.
The second dimension along which information can be characterized is the way relations map from elements of one set to another. For example, relations having functional dependency are those for which each element of a domain maps to only one value in another domain. There are three properties which describe the way relations map from elements of one set to another. Coverage conveys whether every element of a set can be mapped to at least one element of another set. Cardinality expresses the number of elements of a set to which a relation can map from an element of another set. Uniqueness refers to whether a relation maps to a unique value(s) for each element of a set.
While previous examples all involve simple, binary relations, some applications may have relations which map to multiple values, each playing a different role. For example, the geographic-location relation maps between cities and two coordinate values: latitude and longitude. Our approach to this problem is to develop a set of complex data-types which define roles characterizing the relationships among simple binary relations or arguments of complex (n-ary) relations in databases. The set of available data-types has been motivated by the common relationships found in various domains, as well as the existence of popular graphical styles for presenting them. Examples include intervals, statistical abstractions (mean, standard deviation), and 2D coordinate-locations.
Algebraic dependencies among database elements suggest another dimension which can affect presentation design. Dependencies can occur among attributes (relations) or among values within data sets. For example, an organizational database may contain three relations mapping departments to dollar-amounts: materials-costs, labor-costs, and total-costs, where total-costs = materials-costs + labor-costs.
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