A new algorithm spreads information (red) much more efficiently in networks characterized by sparse connections between densely interlinked clusters. Graphic: Christine Daniloff |
As sensors that do things like detect
touch and motion in cell phones get smaller, cheaper, and more reliable,
computer manufacturers are beginning to take seriously the decade-old idea of
“smart dust”—networks of tiny wireless devices that permeate the environment,
monitoring everything from the structural integrity of buildings and bridges to
the activity of live volcanoes. In order for such networks to make collective
decisions, however, they need to integrate information gathered by hundreds or
thousands of devices.
But networks of cheap sensors scattered
in punishing and protean environments are prone to “bottlenecks,” regions of
sparse connectivity that all transmitted data must pass through in order to
reach the whole network. Keren Censor-Hillel, a postdoc at MIT’s Computer
Science and Artificial Intelligence Laboratory, and Hadas Shachnai of Technion—Israel
Institute of Technology presented a new algorithm that handles bottlenecks much
more effectively than its predecessors.
The algorithm is designed to work in
so-called ad hoc networks, in which no one device acts as superintendent,
overseeing the network as a whole. In a network of cheap wireless sensors, for
instance, any given device could fail: its battery could die; its signal could
be obstructed; it could even be carried off by a foraging animal. The network
has to be able to adjust to any device’s disappearance, which means that no one
device can have too much responsibility.
Without a superintendent, the network
has no idea where its bottlenecks are. But that doesn’t matter to Censor-Hillel
and Shachnai’s algorithm. “It never gets to identify the bottlenecks,”
Censor-Hillel says. “It just copes with their existence.”
Consistent inconsistency
The researchers’ analysis of their algorithm makes a few simplifying
assumptions that are standard in the field. One is that communication between
networked devices takes place in rounds. Each round, a device can initiate
communication with only one other device, but it can exchange an unlimited
amount of information with that device and with any devices that contact it.
During each exchange, it passes along all the information it’s received from
any other devices. If the devices are volcano sensors, that information could
be, say, each device’s most recent measurement of seismic activity in its area.
It turns out that if you’re a sensor in
a network with high connectivity—one in which any device can communicate directly
with many of the others—simply selecting a neighboring device at random each
round and sending it all the information you have makes it likely that every
device’s information will permeate the whole network. But take two such highly
connected networks and connect them to each other with only one link—a
bottleneck—and the random-neighbor algorithm no longer works well. On either
side of the bottleneck, it could take a long time for information to work its
way around to the one device that communicates with the other side, and then a
long time for that device to bother to send its information across the
bottleneck.
Censor-Hillel and Shachnai’s algorithm
works by alternating communication strategies from round to round. In the first
round, you select a neighboring device at random and send it all the
information you have—which, since it’s the first round, is limited to the
measurement that you yourself have performed. That same round, however, other
devices may contact you and send you their information. In the second round,
you don’t just select a neighbor at random; you select a neighbor whose
information you have not yet received. In the third round, you again select a
neighbor at random. By the end of that round, since every device on the network
forwards all the information it has, you’ve received not only the measurements
performed by the devices you contacted, nor just the measurements performed by
the devices that contacted you, but measurements performed by neighbors of your
neighbors, and even neighbors of neighbors of neighbors. In the fourth round,
you again select a device whose information you haven’t received; in the fifth,
you select a device at random; and so on.
“The idea is that the randomized steps I
take allow me to spread the information fast within my well-connected subset,”
says Censor-Hillel. But in the alternate rounds, each device tracks down the
devices it hasn’t heard from, ensuring that information will quickly reach all
the devices, including those that communicate across the bottleneck.
According to Alessandro Panconesi, a
professor of computer science at Sapienza Univ. of Rome and an expert on
network analysis, the devices on ad hoc networks tend to have limited
computational power and battery life, so the algorithms they execute must be
very “lightweight.” The new algorithm is “an interesting contribution,”
Panconesi says. “It’s a very simple, locally based algorithm. Essentially, a
node in this network can wake up and start operating by using this algorithm,
and if every node in the network does the same, then essentially you give communication
capability to the entire network.” He points out that the current version of
the algorithm, in which, every round, every device sends all the information
it’s received, wouldn’t be practical: “The algorithm is very expensive in terms
of the information that it needs to exchange.” But he believes that developing
a less bandwidth-intensive version is “not unlikely.” “I’m optimistic,” he
says.
Censor-Hillel agrees that “a major thing
for future work would be to actually get practical bandwidth.” But for the time
being, she’s collaborating with assistant professor of applied mathematics
Jonathan Kelner and with CSAIL grad students Bernhard Haeupler and Petar
Maymounkov to develop an algorithm that performs even better in the idealized
case of unlimited bandwidth. “It’s a major improvement,” she says.
