Let r denote the number of records in the active subset, a the number of attributes, and b the number of bytes needed to store the value of a single attribute. Let p denote the length in pixels of each range slider, f the area in pixels of the starfield, and u the average number of pixels that need to be updated in the starfield display per query (this number depends in a nontrivial way on the size of the starfield, the velocity of the range slider, and the clustering of data in the active subset). Let m denote the number of records in the maximum hit set.
The active subset occupies 
bytes. The rescaled active subset occupies 
bytes. The bucket partition also occupies bytes. The data structures for tight coupling
occupy 
bytes. The data structures for
range histograms occupy 
bytes. The
starfield occupies f bytes.
Setup takes time 
.
There are four components to the time for selection. Determining the
maximum hit set takes time . Sorting
the maximum hit set takes time O(m) (there is no log factor
because we discretize the data). Computing the auxiliary data
structures for tight coupling takes time 
. Computing the auxiliary
data structures for histograms takes time
.
Thus, the total time for selection is
.
There are three components to the time for querying. Tight coupling
takes time O(a). Computing histograms takes time
. Updating the starfield takes time
O(u). Thus the total time for querying is 
.