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Broadcasting in UDG Radio Networks with Unknown Topology PowerPoint Presentation

Broadcasting in UDG Radio Networks with Unknown Topology

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Broadcasting in UDG Radio Networks with Unknown Topology

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Broadcasting in UDG Radio Networks with Unknown Topology

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Broadcasting in UDG Radio Networks with Unknown Topology

WeizmannLiverpoolWeizmannQuébecWeizmannLiverpool

Yuval Emek, Leszek Gąsieniec, Erez Kantor, Andrzej Pelc,David Peleg, Chang Su,

- stations = points in

- transmitting range = 1

- unit disk graph – UDG
- (nodes, edges, paths, …)

- distributed synchronous model

- in every round: transmit or receive

- message heard iff exactly one neighbor transmits

- else: silence or collision (same effect)

(1) no transmission (silence)

(2) single transmission

(3) multiple transmission

v can receive the message from u

v

u

w

vcannotreceive the message

(1) no transmission (silence)

(3) multiple transmission

- collisions cannot be distinguished from silence

v

u

w

vcannotreceive the message

- a unique coordinate system

- each node knows its own coordinates

- does not know the:

- coordinates of any other node

- the number of nodes

- the diameter

- known granularity g =

- inverse of minimum Euclidean distance

- , for every pair of nodes

- typically:d is much smaller then 1 and g is much larger than 1

- a distinguished source node

- source’s message should be heard by all nodes

- remote nodes – use graph’s paths

- connected graphs

- two models are considered:

- conditional wake up: - nodes are initially idle

- wakes up upon hearing a message

- spontaneous wake up:
- – all nodes are awake from the beginning

- execution time =

- #rounds until all nodes hear the source’s message

- decisions of a node on round tdepends only on:

- own coordinates

- t itself

- messages heard so far

- = diameter of the UDG network (in hops)

- = granularity: inverse of min Euclidean distance

- s

- v

- execution time depends on two parameters:

- not Euclidean diameter

- upper bound

- lower bound

- conditionalwake up

- spontaneouswake up

- roughly divided into 2 subareas:

- centralized: complete knowledge, designing fast schedulers

- distributed: local knowledge, designing fast protocols (this work)

- from

- to

- Alon, Bar-Noy, Linial, Peleg ’91: constant D

- Chlamtac, Kutten ’85: formulating the model of radio networks

- Chlamtac, Weinstein ‘91

- Gaber, Mansour ‘95

- Elkin, Kortsarz ‘05

- Gasieniec, Peleg, Xin ‘05

- Kowalski, Pelc (to appear)

- Bar-Yehuda, Goldreich, Itai ’92:

- Kushilevitz, Mansour ’98:

- Czumaj, Rytter ’03:

- unknown topology, no labels, randomized:

- first to study distributed broadcasting (also deterministic)

- (tight!)

- Chlebus, Gasieniec, Gibbons, Pelc, Rytter ’02:

- Kowalski, Pelc ’05:

- unknown topology, knowing own labels, spontaneous wake up, deterministic:

- Kowalski, Pelc ’05: unknown topology, knowing own labels, conditional wake up, deterministic

- Theorem. deterministic broadcasting algorithm A, and choice of parameters D,g, UDG network N of diameter D and granularity g s.t. A requires

- rounds to broadcast in N under the spontaneous wake up model.

- clusters

- k consists of

- cells

- each cell may be occupied with a node or empty

- each cluster contain at least one occupied cell

- source cell (always occupied) in source cluster 0

- clusters

- form a clique

- there is no edge between any and any for |k-i|>1

- the message go from directly to

- from to when only one node from transmit the message

- the message go from directly to

- from to when only one node from transmit the message

- if there exists a node in that heard the message

- then all the nodes of must being heard the source message

- knows the coordinates of the cells

- does not know which cells are occupied and which are empty (except the source)

- knows that there is at least one occupied cell in every cluster

- a typical instruction: “transmit if occupied”

- St = cells scheduled to transmit on round t by A

- decisions are made separately for every k and online based on

- goal: slow down the broadcasting algorithm

- decides for every cell whether occupied or empty

- = number of occupied cells in

- u

- St schedule to transmit

- adversary decide:

- (1) single transmission

- (2) silence / collision

- algorithm can learn?

- what u can learn?

- u

- adversary:

- (1) reveal these cells (occupied/empty)

- (2) report silence / collision

- must be consists with previous reports

- u

- v

- algorithm knows v

- St schedule to transmit by the algorithm

- algorithm can learn whether:

- (1)

- (u hear v)

- (2)

- (u did not hear v)

- u

- adversary:

- (1) reveal these cells

- (2) report silence / collision

- (2) report that collision occur

- must be consists with previous reports

- ti = first round on which the nodes of ireceive the message

- , number of round for delivering the message from ito i+1

- execution time:

- adversary guarantees :

- for ti<cg2

- , for i<cg2/log (g)

- execution time:

- rounds

- rounds

- rounds

- rounds

- chain network

- N1

- N2

- N3

- ND/2

- diameter 2

- Theorem. deterministic broadcasting algorithm A, and g, UDG network N of diameter 2 and granularity g s.t. A requires

- rounds to broadcast in N under the conditional wake up model.

- blocks

- in each block:

- 1>

- auxiliary cells

- opposite each block:

- a target cell

- 1>

- exactly 1 target cell is occupied

- g auxiliary cells

- target

- target cell is outside of the

- transmitting range of any other blocks

- there is at least oneoccupied cell in the block that opposite to the occupied target cell

- the network is connected

- auxiliary

- target

- can no longer guarantee that no messages are being heard

- distinguish silence from collision (stronger model)

- st

- Adversary:

- (1) reveal some cells

- (2) report: collision occur

- (3) report: silence / collision

- execution continues for

- rounds

- dead blocks– all cells are revealed, target cell is empty

- on every round we “kill” at most 1 block and reveal at most 1 cell in each “live” block

- the auxiliary cells of Niis outside the transmitting range of the next source node si+1

- the target cell of Niis inside of the transmitting range of the next source node si+1

- the message must be delivered via target nodes and auxiliary nodes

- execution time:

- upper bound

- lower bound

- conditionalwake up

- spontaneouswake up

- Thank You!!!