 
Summary: Stably computable properties of network graphs
Dana Angluin
James Aspnes
Melody Chan
Michael J. Fischer
Hong Jiang§
RenŽe Peralta
January 17, 2005
Abstract
We consider a scenario in which anonymous, finitestate sensing devices are deployed in
an adhoc communication network of arbitrary 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 optimal 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
