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ETH Zurich – Distributed Computing Group Stephan HolzerETH Zurich – Distributed Computing – www.disco.ethz.ch
Stephan Holzer - ETH ZürichThomas Locher - ABB Switzerland
Yvonne Anne Pignolet - ABB SwitzerlandRoger Wattenhofer - ETH Zürich
Deterministic Multi-Channel
Information Exchange
ETH Zurich – Distributed Computing Group Stephan Holzer
Deterministic Multi-Channel Information Exchange
Problem:n:= # nodes
ETH Zurich – Distributed Computing Group Stephan Holzer
Deterministic Multi-Channel Information Exchange
Problem:n:= # nodesk:= # information Have information
Disseminate to all!?
ETH Zurich – Distributed Computing Group Stephan Holzer
Deterministic Multi-Channel Information Exchange
Problem:
Disseminate to all!?
ETH Zurich – Distributed Computing Group Stephan Holzer
Deterministic Multi-Channel Information Exchange
Problem:
Disseminate to all!?
ETH Zurich – Distributed Computing Group Stephan Holzer
Deterministic Multi-Channel Information Exchange
Problem:n:= # nodes
1
23
4
5
n
Unique IDs 1…n
ETH Zurich – Distributed Computing Group Stephan Holzer
Deterministic Multi-Channel Information Exchange
Problem:
Disseminate to all!?Easy: O(n)
Faster?
ETH Zurich – Distributed Computing Group Stephan Holzer
Deterministic Multi-Channel Information ExchangeI can:
send / receive
reach each node
ETH Zurich – Distributed Computing Group Stephan Holzer
Deterministic Multi-Channel Information ExchangeI can:
send / receive
?reach each node
ETH Zurich – Distributed Computing Group Stephan Holzer
Deterministic Multi-Channel Information Exchange
no collision detection
I can:
send / receive
reach each node
ETH Zurich – Distributed Computing Group Stephan Holzer
Deterministic Multi-Channel Information Exchange
switch channels
no collision detection
I can:
send / receive
reach each node
101 Mhz117 Mhz132 Mhz …
synchronus
ETH Zurich – Distributed Computing Group Stephan Holzer
Deterministic Multi-Channel Information Exchange
switch channels
no collision detection
I can:
send / receive
reach each node
complexitycomputation: freeradio: time 1
synchronus
ETH Zurich – Distributed Computing Group Stephan Holzer
Deterministic Multi-Channel Information Exchange
n:= # nodesk:= # information
Time Channels[GW85]: Ω(k + log n) 1
k
ETH Zurich – Distributed Computing Group Stephan Holzer
Deterministic Multi-Channel Information Exchange
n:= # nodesk:= # information
kTime Channels
[GW85]: Ω(k + log n) 1[HPSW11]: O(k) n
k
ETH Zurich – Distributed Computing Group Stephan Holzer
Deterministic Multi-Channel Information Exchange
n:= # nodesk:= # information
kTime Channels
[GW85]: Ω(k + log n) 1[HPSW11]: O(k) n
Optimal
k
ETH Zurich – Distributed Computing Group Stephan Holzer
Deterministic Multi-Channel Information Exchange
n:= # nodesk:= # information
kTime Channels
[GW85]: Ω(k + log n) 1[HPSW11]: O(k) n
Optimal
????
k
ETH Zurich – Distributed Computing Group Stephan Holzer
Deterministic Multi-Channel Information Exchange
n:= # nodesk:= # information
Range of k [1, ] ( , log n ) [log n , n]Upper boundOn channels O() O() 1
[HPSW11] - Channels needed for time O(k):
ETH Zurich – Distributed Computing Group Stephan Holzer
Deterministic Multi-Channel Information Exchange
n:= # nodesk:= # information
Range of k [1, ] ( , log n ) [log n , n]Upper boundOn channels O() O() 1
[HPSW11] - Channels needed for time O(k):
Range of k [1, log n] (log n , log n loglog n)
[log n loglog n , n- log n)
[n – log n, n]
Upper boundOn channels O() O() O() 1
This paper:
ETH Zurich – Distributed Computing Group Stephan Holzer
Deterministic Multi-Channel Information Exchange
n:= # nodesk:= # information
Range of k [1, ] ( , log n ) [log n , n]Upper boundOn channels O() O() 1
[HPSW11] - Channels needed for time O(k):
Range of k [1, log n] (log n , log n loglog n)
[log n loglog n , n- log n)
[n – log n, n]
Upper boundOn channels O() O() O() 1
This paper:
randomized
ETH Zurich – Distributed Computing Group Stephan Holzer
Deterministic Multi-Channel Information Exchange
n:= # nodesk:= # information
Range of k [1, ] ( , log n ) [log n , n]Upper boundOn channels O() O() 1
[HPSW11] - Channels needed for time O(k):
Range of k [1, log n] (log n , log n loglog n)
[log n loglog n , n- log n)
[n – log n, n]
Upper boundOn channels O() O() O() 1
This paper:
randomized
deterministic
ETH Zurich – Distributed Computing Group Stephan Holzer
Deterministic Multi-Channel Information Exchange
n:= # nodesk:= # information
Range of k [1, ] ( , log n ) [log n , n]Upper boundOn channels O() O() 1
[HPSW11] - Channels needed for time O(k):
Range of k [1, log n] (log n , log n loglog n)
[log n loglog n , n- log n)
[n – log n, n]
Upper boundOn channels O() O() O() 1
This paper:
randomized
deterministic
Optimal?
Optimal?
Optimal?
Optimal?
ETH Zurich – Distributed Computing Group Stephan Holzer
Deterministic Multi-Channel Information Exchange
n:= # nodesk:= # information
Range of k [1, ] ( , log n ) [log n , n]Upper boundOn channels O() O() 1
[HPSW11] - Channels needed for time O(k):
Range of k [1, log n] (log n , log n loglog n)
[log n loglog n , n- log n)
[n – log n, n]
Upper boundOn channels O() O() O() 1Lower boundOn channels Ω() Ω() Ω(log ) 1
This paper:
randomized
deterministic
k
ETH Zurich – Distributed Computing Group Stephan Holzer
Deterministic Multi-Channel Information Exchange
Main ingredient:
Specially taylored graphs.
ETH Zurich – Distributed Computing Group Stephan Holzer
Deterministic Multi-Channel Information Exchange
Main ingredient:
Specially taylored graphs.(Inspired by use of lossless expanders in [CK08])
ETH Zurich – Distributed Computing Group Stephan Holzer
Deterministic Multi-Channel Information Exchange
Main ingredient:
Specially taylored graphs.(Inspired by use of lossless expanders in [CK08])
Topology: Still single hop.Graphs used to select channel.
ETH Zurich – Distributed Computing Group Stephan Holzer
Deterministic Multi-Channel Information Exchange
7
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1V
W
Bipartite :
node IDs new names
ETH Zurich – Distributed Computing Group Stephan Holzer
Deterministic Multi-Channel Information Exchange
7
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1V
W
Bipartite :
node IDs new names
ETH Zurich – Distributed Computing Group Stephan Holzer
Deterministic Multi-Channel Information Exchange
Matching Graphs:• Nodes in V have degee V
W
Δ
ETH Zurich – Distributed Computing Group Stephan Holzer
Deterministic Multi-Channel Information Exchange
Matching Graphs:• Nodes in V have degee • Fixed order of edges
VW
4123
ETH Zurich – Distributed Computing Group Stephan Holzer
Deterministic Multi-Channel Information Exchange
Matching Graphs:• Nodes in V have degee • Fixed order of edges
• For any of size at most k there is
at least nodes in X have a unique i-neighbor.
VW
4123
ETH Zurich – Distributed Computing Group Stephan Holzer
Deterministic Multi-Channel Information Exchange
Matching Graphs:• Nodes in V have degee • Fixed order of edges
• For any of size at most k there is
at least nodes in X have a unique i-neighbor.
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1
VW
i
ihave uniquei-neighbor
ETH Zurich – Distributed Computing Group Stephan Holzer
Deterministic Multi-Channel Information Exchange
Matching Graphs:• Nodes in V have degee • Fixed order of edges
• For any of size at most k there is
at least nodes in X have a unique i-neighbor.
7
6
5
4
3
2
1
VW
i
ihave uniquei-neighbor
ETH Zurich – Distributed Computing Group Stephan Holzer
Deterministic Multi-Channel Information Exchange
Matching Graphs:• Nodes in V have degee • Fixed order of edges
• For any of size at most k there is
at least nodes in X have a unique i-neighbor.
7
6
5
4
3
2
1 1
1
1
2
1
2
2
2
VW
ETH Zurich – Distributed Computing Group Stephan Holzer
Deterministic Multi-Channel Information Exchange
Matching Graphs:• Nodes in V have degee • Fixed order of edges
• For any of size at most k there is
at least nodes in X have a unique i-neighbor.
7
6
5
4
3
2
1 1
1
1
2
1
2
2
2
VW
X
ETH Zurich – Distributed Computing Group Stephan Holzer
Deterministic Multi-Channel Information Exchange
Matching Graphs:• Nodes in V have degee • Fixed order of edges
• For any of size at most k there is
at least nodes in X have a unique i-neighbor.
7
6
5
4
3
2
1 1
1
1
1
VW
X
ETH Zurich – Distributed Computing Group Stephan Holzer
Deterministic Multi-Channel Information Exchange
Matching Graphs:• Nodes in V have degee • Fixed order of edges
• For any of size at most k there is
at least nodes in X have a unique i-neighbor.
7
6
5
4
3
2
1 1
1
1
1
VW
XBAD
ETH Zurich – Distributed Computing Group Stephan Holzer
Deterministic Multi-Channel Information Exchange
Matching Graphs:• Nodes in V have degee • Fixed order of edges
• For any of size at most k there is
at least nodes in X have a unique i-neighbor.
7
6
5
4
3
2
1 1
1
1
2
1
2
2
2
VW
X
ETH Zurich – Distributed Computing Group Stephan Holzer
Deterministic Multi-Channel Information Exchange
Matching Graphs:• Nodes in V have degee • Fixed order of edges
• For any of size at most k there is
at least nodes in X have a unique i-neighbor.
7
6
5
4
3
2
122
2
2
VW
X
ETH Zurich – Distributed Computing Group Stephan Holzer
Deterministic Multi-Channel Information Exchange
Matching Graphs:• Nodes in V have degee • Fixed order of edges
• For any of size at most k there is
at least nodes in X have a unique i-neighbor.
7
6
5
4
3
2
122
2
2
VW
XGOOD
ETH Zurich – Distributed Computing Group Stephan Holzer
Deterministic Multi-Channel Information Exchange
Matching Graphs:• Nodes in V have degee • Fixed order of edges
• For any of size at most k there is
at least nodes in X have a unique i-neighbor.
7
6
5
4
3
2
1 1
1
1
1
VW
X
ETH Zurich – Distributed Computing Group Stephan Holzer
Deterministic Multi-Channel Information Exchange
Matching Graphs:• Nodes in V have degee • Fixed order of edges
• For any of size at most k there is
at least nodes in X have a unique i-neighbor.
7
6
5
4
3
2
1 1
1
1
1
VW
X
ETH Zurich – Distributed Computing Group Stephan Holzer
Deterministic Multi-Channel Information Exchange
Matching Graphs:• Nodes in V have degee • Fixed order of edges
• For any of size at most K there is
at least nodes in X have a unique i-neighbor.
exist if 7
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2
1 1
1
1
2
1
2
2
2
VW
ETH Zurich – Distributed Computing Group Stephan Holzer
Deterministic Multi-Channel Information Exchange
What are these graphs good for?
ETH Zurich – Distributed Computing Group Stephan Holzer
Deterministic Multi-Channel Information Exchange
What are these graphs good for?
Renaming
ETH Zurich – Distributed Computing Group Stephan Holzer
Deterministic Multi-Channel Information Exchange
What are these graphs good for?
Renaming
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1 1
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1
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VW
ETH Zurich – Distributed Computing Group Stephan Holzer
Deterministic Multi-Channel Information Exchange
What are these graphs good for?
Renaming
• To each of the k «reporters» we can assing a new unique name in |W| in time O( using |W| channels.
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VW
ETH Zurich – Distributed Computing Group Stephan Holzer
Deterministic Multi-Channel Information Exchange
What is renaming good for?
ETH Zurich – Distributed Computing Group Stephan Holzer
Deterministic Multi-Channel Information Exchange
What is renaming good for?Assignment of reporters to channels!
ETH Zurich – Distributed Computing Group Stephan Holzer
Deterministic Multi-Channel Information Exchange
What is renaming good for?Assignment of reporters to channels!
Example: k < log n
ETH Zurich – Distributed Computing Group Stephan Holzer
Deterministic Multi-Channel Information Exchange
What is renaming good for?Assignment of reporters to channels!
Example: k < log n
n
Original names
ETH Zurich – Distributed Computing Group Stephan Holzer
Deterministic Multi-Channel Information Exchange
What is renaming good for?Assignment of reporters to channels!
Example: k < log n
n
Original names
O()
New namesof reporters
ETH Zurich – Distributed Computing Group Stephan Holzer
Deterministic Multi-Channel Information Exchange
n O()
Original names
New namesof reporters
ETH Zurich – Distributed Computing Group Stephan Holzer
Deterministic Multi-Channel Information Exchange
n:= # nodesk:= # information
n O()
Original names
New namesof reporters
ETH Zurich – Distributed Computing Group Stephan Holzer
Deterministic Multi-Channel Information Exchange
n:= # nodesk:= # information
Time: O( k )
𝑆𝑖𝑧𝑒 :𝑛 /2n O()
Original names
New namesof reporters
ETH Zurich – Distributed Computing Group Stephan Holzer
Deterministic Multi-Channel Information Exchange
n:= # nodesk:= # information
𝑆𝑖𝑧𝑒 :𝑛 /2n O()
Original names
New namesof reporters
ETH Zurich – Distributed Computing Group Stephan Holzer
Deterministic Multi-Channel Information Exchange
n:= # nodesk:= # information
𝑆𝑖𝑧𝑒 :𝑛 /2n O()
Original names
New namesof reporters
ETH Zurich – Distributed Computing Group Stephan Holzer
Deterministic Multi-Channel Information Exchange
n:= # nodesk:= # information
𝑆𝑖𝑧𝑒 :𝑛 /2
Send on channel “new name” .
n O()
Original names
New namesof reporters
ETH Zurich – Distributed Computing Group Stephan Holzer
Deterministic Multi-Channel Information Exchange
n:= # nodesk:= # information
𝑆𝑖𝑧𝑒 :𝑛 /2
Send on channel “new name” .Send on channel “new name” .
n O()
Original names
New namesof reporters
ETH Zurich – Distributed Computing Group Stephan Holzer
Deterministic Multi-Channel Information Exchange
n:= # nodesk:= # information
Send on channel “new name” .Send on channel “new name” .
𝑆𝑖𝑧𝑒 :𝑛 /2
ETH Zurich – Distributed Computing Group Stephan Holzer
Deterministic Multi-Channel Information Exchange
n:= # nodesk:= # information
Send on channel “new name” .Send on channel “new name” .
𝑆𝑖𝑧𝑒 :𝑛 /2 Example: 3 channels
ETH Zurich – Distributed Computing Group Stephan Holzer
Deterministic Multi-Channel Information Exchange
n:= # nodesk:= # information
Channel 3
Example: 3 channels
Channel 1
{1,2}{1,3 }{2,3 }
ETH Zurich – Distributed Computing Group Stephan Holzer
Deterministic Multi-Channel Information Exchange
n:= # nodesk:= # information
Channel 3
Example: 3 channels
Channel 1Send 2 times
{1,2}{1,3 }{2,3 }
ETH Zurich – Distributed Computing Group Stephan Holzer
Deterministic Multi-Channel Information Exchange
n:= # nodesk:= # information
Channel 3
Example: 3 channels
Channel 1Send 2 times
{1,2}{1,3 }{2,3 }
ETH Zurich – Distributed Computing Group Stephan Holzer
Deterministic Multi-Channel Information Exchange
{1,2}{1,3 }{2,3 }
n:= # nodesk:= # information
Channel 3
Example: 3 channels
Channel 1Send 2 times
ETH Zurich – Distributed Computing Group Stephan Holzer
Deterministic Multi-Channel Information Exchange
n:= # nodesk:= # information
Channel 3
Example: 3 channels
Channel 1Send 2 times
{1,3 }
ETH Zurich – Distributed Computing Group Stephan Holzer
Deterministic Multi-Channel Information Exchange
n:= # nodesk:= # information
Unique Subset
Channel 3
Example: 3 channels
Channel 1Send 2 times
{1,3 }
ETH Zurich – Distributed Computing Group Stephan Holzer
Deterministic Multi-Channel Information Exchange
n:= # nodesk:= # information
Unique Subset
Channel 3
Example: 3 channels
Channel 1Send 2 times
{1,3 }
ETH Zurich – Distributed Computing Group Stephan Holzer
Deterministic Multi-Channel Information Exchange
n:= # nodesk:= # information
Unique Subset
Channel 3
Example: 3 channels
Channel 1Send 2 times
{1,3 }
ETH Zurich – Distributed Computing Group Stephan Holzer
Deterministic Multi-Channel Information Exchange
Unique Subset
Channel 3
Example: 3 channels
Channel 1Send k times
{1,3 } O( k )
n:= # nodesk:= # information
ETH Zurich – Distributed Computing Group Stephan Holzer
Deterministic Multi-Channel Information Exchange
O( k )
Send on channel “new name” .Send on channel “new name” .
Range of k [1, log n] (log n , log n loglog n)
[log n loglog n , n- log n)
[n – log n, n]
Upper boundOn channels O() O() O() 1Lower boundOn channels Ω() Ω() Ω(log ) 1
ETH Zurich – Distributed Computing Group Stephan Holzer
Deterministic Multi-Channel Information Exchange
n O()
Original names
New namesof reporters
O() channels
ETH Zurich – Distributed Computing Group Stephan Holzer
Deterministic Multi-Channel Information Exchange
in Summary … Detect / Disseminate Information!
101 Mhz117 Mhz132 Mhz …𝜣 (𝒌)
{1,3 }7
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11
1
1
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1
2
2
2
VW
X
Range of k [1, log n] (log n , log n loglog n)
[log n loglog n , n- log n)
[n – log n, n]
Upper boundOn channels O() O() O() 1Lower boundOn channels Ω() Ω() Ω(log ) 1
ETH Zurich – Distributed Computing Group Stephan HolzerETH Zurich – Distributed Computing – www.disco.ethz.ch
Stephan Holzer - ETH ZürichThomas Locher - ABB Switzerland
Yvonne Anne Pignolet - ABB SwitzerlandRoger Wattenhofer - ETH Zürich
Thank You!Questions & Comments?
ETH Zurich – Distributed Computing Group Stephan HolzerETH Zurich – Distributed Computing – www.disco.ethz.ch
Stephan Holzer - ETH ZürichThomas Locher - ABB Switzerland
Yvonne Anne Pignolet - ABB SwitzerlandRoger Wattenhofer - ETH Zürich
Thank You!Questions & Comments?