Consider the Locations, Products, and Sales relations in Figure $25\mathrm{.}2$

$1.$ To decide whether to materialize a view, what factors do we need to consider?

$2.$ Assume we have defined the following materialized view:

Select L$.$state, S$.$sales

FROM Locations L$,$ Sales S

WHERE S$.$locid$=$L$.$locid

$($a$)$ Describe what auxiliary information the algorithm for incremental view maintenance from Section $25\mathrm{.}10\mathrm{.}1$ maintains and how this data helps in maintaining the view incrementally.