 
Summary: Stably computable properties of network graphs
Dana Angluin, James Aspnes, Melody Chan, Michael J. Fischer, Hong Jiang,
and RenŽe Peralta
Yale University
Abstract. We consider a scenario in which anonymous, finitestate sens
ing devices are deployed in an adhoc communication network of arbi
trary size and unknown topology, and explore what properties of the
network graph can be stably computed by the devices. We show that
they can detect whether the network has degree bounded by a constant
d, and, if so, organize a computation that achieves asymptotically opti
mal linear memory use. We define a model of stabilizing inputs to such
devices and show that a large class of predicates of the multiset of final
input values are stably computable in any weaklyconnected network.
We also show that nondeterminism in the transition function does not
increase the class of stably computable predicates.
1 Introduction
In some applications, a large number of sensors will be deployed without fine
control of their locations and communication patterns in the target environment.
To enable the distributed gathering and processing of information, the sensors
must constitute themselves into an adhoc network and use it effectively. A fun
