  We investigate a zone based approach for the reachability problem in timed
automata. The challenge is to alleviate the size explosion of the search space
when considering networks of timed automata working in parallel. In the timed
setting this explosion is particularly visible as even different interleavings
of local actions of processes may lead to different zones. Salah et al. in 2006
have shown that the union of all these different zones is also a zone. This
observation was used in an algorithm which from time to time detects and
aggregates these zones into a single zone.
  We show that such aggregated zones can be calculated more efficiently using
the local time semantics and the related notion of local zones proposed by
Bengtsson et al. in 1998. Next, we point out a flaw in the existing method to
ensure termination of the local zone graph computation. We fix this with a new
algorithm that builds the local zone graph and uses abstraction techniques over
(standard) zones for termination. We evaluate our algorithm on standard
examples. On various examples, we observe an order of magnitude decrease in the
search space. On the other examples, the algorithm performs like the standard
zone algorithm.
