Summary: Stably computable properties of network graphs
Dana Angluin, James Aspnes, Melody Chan, Michael J. Fischer, Hong Jiang,
and RenŽe Peralta
Abstract. We consider a scenario in which anonymous, finite-state sens-
ing devices are deployed in an ad-hoc 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 weakly-connected network.
We also show that nondeterminism in the transition function does not
increase the class of stably computable predicates.
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 ad-hoc network and use it effectively. A fun-