Distributed Software Systems Group

1
Programming a Sensor Network as an Amorphous
Medium

• Jonathan Bachrach and Jacob Beal
• DCOSS 06
• Pruet _at_ DSSG

bachrach06programming
2
Outline

• Introduction
• Programming Amorphous Media
• Approximating Amorphous Media

3
Introduction

• To develop an application on a wireless sensor
  network, application developers should focus on
  writing code in the application domain level
• rather than developing in network or individual
  sensor node level.
• The spatial nature of sensor network applications
  can be naturally expressed in terms of global
  behavior of an Amorphous medium.
• Amorphous medium is a theoretical continuous
  computational material which fills space of
  interest.
• Every point in the medium is an independent
  computational device.
• Each point executes the same code, but can behave
  differently based on local condition.
• Each point has a neighborhood of devices nearby
  whose state it can access.

4
Introduction

• Amorphous medium abstraction separates sensor
  network problem into two largely independent
  domains.
• above the abstraction barrier, developer has to
  concern with the long-range coordination (global)
  and concise description of applications.
• below the barrier, developer has to concern with
  the fast, efficient and robust communication
  between neighboring devices.

5
Programming Amorphous Media

• Programs in Amorphous Media are written in Proto
  programming language.
• A program in Proto compute on an amorphous medium
  by manipulating fields.
• A field is a map assigning a value to each point
  in the space.
• When executed, the program is evaluated against
  the space at regular intervals to produce a
  stream of output fields.
• Primitives in Proto are either
• terminals which produce fields, or
• operators which calculate an output field from
  input fields.

6
Programming in Amorphous Media

• a) create a field of value 2.
• b) create a field by adding the value of input
  fields pointwise.
• c) two input values are selected pointwise based
  on the boolean condition of the third field.

7
Programming in Amorphous Media

• d) value 2 and 5 are assigned to two different
  fields, the their value are sum to create the
  third field.
• e) operator sq is defined as x x
• f) a field with value 9 is created by input a
  field with value 3 to operator sq.

8
Proto

• Primitives in Proto are composed to form complex
  expression by connecting outputs to inputs to
  form a directed graph.
• LISP-like syntax is used, e.g. ( 2 5)
• A new primitive can be created by a fragment of
  graph, using lambda expression.
• E.g. (lambda (x) ( x x))
• A named lambda can be defined using def
• E.g. (def sq (a) ( a a))
• Syntax (def name(input) (operation))

9
Proto

• Instead of exchanging messages between neighbors
  to perform area-based calculation,
• e.g. find an average sensor reading among all
  neighbors,
• Proto provides implicit communication through the
  reduce-nbrs operator.
• reduce-nbrs summarizes the values in the
  neighborhood using a uncountable sets(continuous)
  quantifier.
• Five quantifiers are implemented integral (sum),
  forall and exists (AND and OR), limsup and liminf
  (min and max)
• E.g.,
• (def local-average(v)
• ( /
• (reduce-nbrs v integral) //sum of value v
  of all neighbors
• (reduce-nbrs 1 integral) //number of
  neighbors
• )
• )

10
Proto

• Proto also provides operators for measuring
  distance in space and time, nbr-range and
  nbr-lag, respectively.
• Persistent state is established using delay
  loops.
• Proto is functional programming language which
  does not have side-effect.
• The delay loop can hold the output from this
  round to the next round.
• E.g. to define a discrete-time integrator
• (def integrator (x) (letfed ((v 0 ( x v))) v))

Output field
performed each round
initial field
internal state field
11
Proto

• Example gradient operator
• Create gradient toward a point
• (def gradient (src)
• (letfed
• ((n infinity
• ( 1 (mux src 0
• (reduce-nbrs
• ( n nbr-range)
• limsup
• )
• )
• )
• ))
• (- n 1)
• )
• )

n 0
n 5
5
20
5
5
n 20
n 10
n inf
n inf
n 0
n 5
n inf
n inf
n 15
n 10
n 0
n inf
n inf
n inf
n 0
n 5
n 20
n inf
12
Proto

• if operator restricts the field against which an
  expression is evaluated.
• (def dilate (r source) (lt (gradient source) r))
• (def bound (source max boundary)
• (if (not boundary) (dilate max source)))
• The dilation runs only within the boundaries
  containing the source.

13
Approximating Amorphous Media

• In order to execute Proto program on a sensor
  network, the kernel(VM) has to
• approximately simulates the amorphous medium
• approximates global evaluation with local code,
• approximates continuous space with discrete
  devices.
• Rather than attempt to synchronize the operations
  between devices,
• each device executes independently once every t
  seconds by its own clock.
• So, each program has to be executed within t
  seconds.
• The program is executed at the base station
  first, then distributed to the sensor network
  dynamically.
• For each operation that requires information from
  neighboring nodes, e.g. reduce-nbrs or nbr-range,
  sensor nodes broadcast a request and wait for the
  respond from neighbors.
• The integral quantifier sums the values from the
  neighborhood, weighted by the estimated area each
  represents.