Future networks must be adequately equipped to handle multipoint commu
nication in a fast and economical manner, Services requiring such supp
ort include desktop video conferencing, tele-classrooms, distributed d
atabase applications, etc, In networks employing the asynchronous tran
sfer mode (ATM) technology, routing a multicast is achieved by constru
cting a minimum cost tree that spans the source and all the destinatio
ns, When the network is modeled as a weighted, undirected graph, the p
roblem is that of finding a minimal Steiner tree for the graph, given
a set of destinations, The problem is known to be NP-complete. Consequ
ently, several heuristics exist which provide approximate solutions to
the Steiner problem in networks, In this paper, we show how the rando
m neural network (RNN) can be used to significantly improve the qualit
y of the Steiner trees delivered by the best available heuristics whic
h are the minimum spanning tree heuristic and the average distance heu
ristic. We provide an empirical comparison and find that the heuristic
s which are modified using the neural network yield significantly impr
oved trees.