We consider the problem of speeding up the incremental maintenance of
materialized views defined by conjunctive queries (CQ) over external
base relations, when querying these base relations is {\em expensive}.
Our approach consists of detecting, {\em without} using the base
relations, situations where a view either is not affected by a base
update (VDU) or can be maintained using only the views in the
warehouse (VSM). We are doing runtime optimization of view
maintenance, since the tests take the current state of the warehouse
database into account.  Testing VSM for CQ views in general is known
to be co-NP-complete in the size of the views, and testing VDU is
conjectured to be as hard. In this paper, we identify important
subclasses of CQ views for which VDU and VSM can be tested {\em
completely} and {\em efficiently}, using only a small constant number
of view lookups. This result is significant because, by maintaining
indexes on selected view attributes, we can speed up view maintenance
practically without incurring any substantial overhead.  For more
general CQ views, we show sufficient tests for VDU and VSM that have
comparable efficiency. To demonstrate the performance of our method,
we implement a view manager in Oracle PL-SQL which maintains a simple
view under various synthetic update streams and under various delays
in querying the base relations. Our results clearly show situations
where tremendous speedup can be achieved. While further performance
studies remain to be done, we believe our approach has a great
potential to significantly speed up incremental data warehouse maintenance.