broadcasting protocol for an amorphous computer lukáš petrů mff uk, prague jiří wiedermann ics...
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Broadcasting Protocol for an Broadcasting Protocol for an Amorphous ComputerAmorphous Computer
Lukáš PetrůMFF UK, Prague
Jiří WiedermannICS AS CR
OutlineOutline
MotivationModel of an Amorphous computerProtocol SendProtocol BroadcastConclusion
Device MiniaturizationDevice Miniaturization
Technology allows producing very small energy efficient devices (MEMS)
They can be built in large numbersCan communicate via wireless radio
→ Wireless sensor networks
→ Amorphous computers
Wireless Sensor NetworkWireless 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
Amorphous Computer (pict.)Amorphous Computer (pict.)
A bag containing a large number of computing elements
Amorphous ComputerAmorphous Computer
Amorphous ComputerAmorphous Computer
Amorphous Computer (AC)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
Model of an ACModel of an AC
No synchronizationNo collision detection (no message is
received in case of collision)Special node IO-portNo addresses
NodeNode
Registers
Size O(log N) bits
Control unit
…
Random numberInput
Output
Model of an ACModel 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
Random TopologyRandom Topology
When the node topology is random, what are the consequences on the communication possibility?
Is communication possible?Under what conditions?
Random TopologyRandom Topology
Low density
Random TopologyRandom Topology
Medium density
Random TopologyRandom Topology
High density
AssumptionsAssumptions
Assume that network connectivity graph contains one large component– Some nodes may not be part of the component
N = size of the graph componentQ = maximum neighbourhood sizeD = diameter of the graph component
Sending to NeighboursSending to Neighbours
Protocol SendProtocol 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 node’s neighbours;given ε – the maximum allowed probability of failed transmission is known
Protocol SendProtocol Send
Let p = 1/(Q+1); k = O(Q · log(1/ε))
procedure Send(m : message,p : probability) {For i := 1 to k do {
Wait for time 2T;With probability p do
Send message m;}
}
Protocol SendProtocol 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 ε.The protocol works in time O( Q log (1/ε) ).
BroadcastingBroadcasting
Protocol BroadcastProtocol 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 size;Q – node neighbourhood size upper bound;ε – the maximum allowed probability of broadcast algorithm error
Protocol BroadcastProtocol Broadcast
procedure Broadcast(N : integer) {var m, m_last : messageLoop forever {
receive(m);If m != m_last {
Send(m, ε/N);m_last = m;
}}
}
Protocol BroadcastProtocol Broadcast
Theorem:
On a network of diameter D, algorithm Broadcast will run in timeO(D · Q · log (N/ε)). The probability of algorithm failure is at most ε>0.
ConclusionConclusion
We have …
defined a formal model of ACdeveloped a randomized broadcasting
algorithmderived its time complexity
Future workFuture work
Describe simulation of other theoretical models (Turing machine, RAM)
Consider moving nodes – flying amorphous computer