Broadcasting Protocol for an Amorphous Computer

1
Broadcasting Protocol for an Amorphous Computer

• Lukáš PetruMFF UK, Prague
• Jirí WiedermannICS AS CR

2
Outline

• Motivation
• Model of an Amorphous computer
• Protocol Send
• Protocol Broadcast
• Conclusion

3
Device Miniaturization

• Technology allows producing very small energy
  efficient devices (MEMS)
• They can be built in large numbers
• Can communicate via wireless radio
• ? Wireless sensor networks
• ? Amorphous computers

4
Wireless Sensor Network

• A large number of devices is randomly distributed
  in an area of interest
• Each device is self-contained employing sensors,
  CPU, memory, controller, wireless transceiver and
  power source
• Sensors measuring light intensity, temperature,
  humidity, , or intrusion detectors, etc.
• Data from all devices on the network are gathered
  in base station

5
Amorphous Computer (pict.)
A bag containing a large number of computing
elements
6
Amorphous Computer
7
Amorphous Computer
8
Amorphous Computer (AC)

• Idea of a computing machine built from a large
  number of identical parts
• Differences from wireless networks
• only CPU with a severely limited memory
• Random topology
• All devices are identical (no id numbers)
• No signal collision detection

9
Model of an AC

• No synchronization
• No collision detection (no message is received in
  case of collision)
• Special node IO-port
• No addresses

10
Node
Random number
Input
Output

Control unit
Registers
Size O(log N) bits
11
Model of an AC

• Amorphous computer A(N, P, A, r, T)
• N number of nodes (processors) each node is a
  RAM with registers of size O(log N) bits has
  random number generator
• P, A a process P randomly distributes nodes in
  a planar area A
• r radio range nodes within distance r are
  neighbours
• T duration of one radio transmission

12
Random Topology

• When the node topology is random, what are the
  consequences on the communication possibility?
• Is communication possible?
• Under what conditions?

13
Random Topology
Low density
14
Random Topology
Medium density
15
Random Topology
High density
16
Assumptions

• Assume that network connectivity graph contains
  one large component
• Some nodes may not be part of the component
• N size of the graph component
• Q maximum neighbourhood size
• D diameter of the graph component

17
Sending to Neighbours
18
Protocol Send

• An algorithm that determines how a node transmits
  a message to its neighbours
• Operates in an uncoordinated network of
  undistinguishable nodes that are not synchronized
• Assumptions given Q An upper bound on the
  number of nodes neighboursgiven e the
  maximum allowed probability of failed
  transmission is known

19
Protocol Send

• Let p 1/(Q1) k O(Q log(1/e))
• procedure Send(m message,
• p probability)
• For i 1 to k do
• Wait for time 2T
• With probability p do
• Send message m

20
Protocol Send

• Theorem
• If all nodes of the network use algorithm Send,
  then the probability that a message fails to be
  delivered from a sender to any of its neighbours
  is at most e.The protocol works in time O( Q log
  (1/e) ).

21
Broadcasting
22
Protocol Broadcast

• is used to deliver the same message to all nodes
  in the network
• A simple protocol for node-to-node communication
  when no routing information is available
• Assumptions given N the network sizeQ node
  neighbourhood size upper bounde the maximum
  allowed probability of broadcast algorithm error

23
Protocol Broadcast

• procedure Broadcast(N integer)
• var m, m_last message
• Loop forever
• receive(m)
• If m ! m_last
• Send(m, e/N)
• m_last m

24
Protocol Broadcast

• Theorem
• On a network of diameter D, algorithm Broadcast
  will run in timeO(D Q log (N/e)). The
  probability of algorithm failure is at most egt0.

25
Conclusion

• We have
• defined a formal model of AC
• developed a randomized broadcasting algorithm
• derived its time complexity

26
Future work

• Describe simulation of other theoretical models
  (Turing machine, RAM)
• Consider moving nodes flying amorphous computer