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ETH Zurich – Distributed Computing Group Stephan HolzerETH Zurich – Distributed Computing – www.disco.ethz.ch Stephan Holzer - ETH Zürich Thomas Locher - ABB Switzerland Yvonne Anne Pignolet - ABB Switzerland Roger Wattenhofer - ETH Zürich TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAA A A AA AA Deterministic Multi-Channel Information Exchange
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ETH Zurich – Distributed Computing Group Stephan Holzer Deterministic Multi-Channel Information Exchange Problem : n:= # nodes
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ETH Zurich – Distributed Computing Group Stephan Holzer Deterministic Multi-Channel Information Exchange Problem : n:= # nodes k:= # information Have information Disseminate to all! ?
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ETH Zurich – Distributed Computing Group Stephan Holzer Deterministic Multi-Channel Information Exchange Problem : Disseminate to all! ?
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ETH Zurich – Distributed Computing Group Stephan Holzer Deterministic Multi-Channel Information Exchange Problem : Disseminate to all! ?
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ETH Zurich – Distributed Computing Group Stephan Holzer Deterministic Multi-Channel Information Exchange Problem : n:= # nodes 1 2 3 4 5 n Unique IDs 1…n
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ETH Zurich – Distributed Computing Group Stephan Holzer Deterministic Multi-Channel Information Exchange Problem : Disseminate to all! ? Easy: O(n) Faster?
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ETH Zurich – Distributed Computing Group Stephan Holzer Deterministic Multi-Channel Information Exchange I can: send / receive reach each node
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ETH Zurich – Distributed Computing Group Stephan Holzer Deterministic Multi-Channel Information Exchange I can: send / receive ? reach each node
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ETH Zurich – Distributed Computing Group Stephan Holzer Deterministic Multi-Channel Information Exchange no collision detection I can: send / receive reach each node
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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 Mhz 117 Mhz 132 Mhz … synchronus
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ETH Zurich – Distributed Computing Group Stephan Holzer Deterministic Multi-Channel Information Exchange switch channels no collision detection I can: send / receive reach each node complexity computation: free radio: time 1 synchronus
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ETH Zurich – Distributed Computing Group Stephan Holzer Deterministic Multi-Channel Information Exchange n:= # nodes k:= # information TimeChannels [GW85]:Ω(k + log n)1 k
![ETH Zurich – Distributed Computing Group Stephan Holzer Deterministic Multi-Channel Information Exchange n:= # nodes k:= # information TimeChannels [GW85]:Ω(k + log n)1 k](http://images.slideplayer.com./47/11690858/slides/slide_13.jpg "ETH Zurich – Distributed Computing Group Stephan Holzer Deterministic Multi-Channel Information Exchange n:= # nodes k:= # information TimeChannels [GW85]:Ω(k + log n)1 k")
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ETH Zurich – Distributed Computing Group Stephan Holzer Deterministic Multi-Channel Information Exchange n:= # nodes k:= # information k TimeChannels [GW85]:Ω(k + log n)1 [HPSW11]:O(k)n k
![ETH Zurich – Distributed Computing Group Stephan Holzer Deterministic Multi-Channel Information Exchange n:= # nodes k:= # information k TimeChannels [GW85]:Ω(k + log n)1 [HPSW11]:O(k)n k](http://images.slideplayer.com./47/11690858/slides/slide_14.jpg "ETH Zurich – Distributed Computing Group Stephan Holzer Deterministic Multi-Channel Information Exchange n:= # nodes k:= # information k TimeChannels [GW85]:Ω(k + log n)1 [HPSW11]:O(k)n k")
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ETH Zurich – Distributed Computing Group Stephan Holzer Deterministic Multi-Channel Information Exchange n:= # nodes k:= # information k TimeChannels [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:= # nodes k:= # information k TimeChannels [GW85]:Ω(k + log n)1 [HPSW11]:O(k)n Optimal k](http://images.slideplayer.com./47/11690858/slides/slide_15.jpg "ETH Zurich – Distributed Computing Group Stephan Holzer Deterministic Multi-Channel Information Exchange n:= # nodes k:= # information k TimeChannels [GW85]:Ω(k + log n)1 [HPSW11]:O(k)n Optimal k")
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ETH Zurich – Distributed Computing Group Stephan Holzer Deterministic Multi-Channel Information Exchange n:= # nodes k:= # information k TimeChannels [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:= # nodes k:= # information k TimeChannels [GW85]:Ω(k + log n)1 [HPSW11]:O(k)n Optimal .](http://images.slideplayer.com./47/11690858/slides/slide_16.jpg "k.")
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ETH Zurich – Distributed Computing Group Stephan Holzer Deterministic Multi-Channel Information Exchange n:= # nodes k:= # information Range of k[log n, n] Upper bound On channels 1 [HPSW11] - Channels needed for time O(k):
![ETH Zurich – Distributed Computing Group Stephan Holzer Deterministic Multi-Channel Information Exchange n:= # nodes k:= # information Range of k[log n, n] Upper bound On channels 1 [HPSW11] - Channels needed for time O(k):](http://images.slideplayer.com./47/11690858/slides/slide_17.jpg "ETH Zurich – Distributed Computing Group Stephan Holzer Deterministic Multi-Channel Information Exchange n:= # nodes k:= # information Range of k[log n, n] Upper bound On channels 1 [HPSW11] - Channels needed for time O(k):")
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ETH Zurich – Distributed Computing Group Stephan Holzer Deterministic Multi-Channel Information Exchange n:= # nodes k:= # information Range of k[log n, n] Upper bound On channels 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 bound On channels 1 This paper:
![ETH Zurich – Distributed Computing Group Stephan Holzer Deterministic Multi-Channel Information Exchange n:= # nodes k:= # information Range of k[log n, n] Upper bound On channels 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 bound On channels 1 This paper:](http://images.slideplayer.com./47/11690858/slides/slide_18.jpg "ETH Zurich – Distributed Computing Group Stephan Holzer Deterministic Multi-Channel Information Exchange n:= # nodes k:= # information Range of k[log n, n] Upper bound On channels 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 bound On channels 1 This paper:")
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ETH Zurich – Distributed Computing Group Stephan Holzer Deterministic Multi-Channel Information Exchange n:= # nodes k:= # information Range of k[log n, n] Upper bound On channels 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 bound On channels 1 This paper: randomized
![ETH Zurich – Distributed Computing Group Stephan Holzer Deterministic Multi-Channel Information Exchange n:= # nodes k:= # information Range of k[log n, n] Upper bound On channels 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 bound On channels 1 This paper: randomized](http://images.slideplayer.com./47/11690858/slides/slide_19.jpg "ETH Zurich – Distributed Computing Group Stephan Holzer Deterministic Multi-Channel Information Exchange n:= # nodes k:= # information Range of k[log n, n] Upper bound On channels 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 bound On channels 1 This paper: randomized")
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ETH Zurich – Distributed Computing Group Stephan Holzer Deterministic Multi-Channel Information Exchange n:= # nodes k:= # information Range of k[log n, n] Upper bound On channels 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 bound On channels 1 This paper: randomized deterministic
![ETH Zurich – Distributed Computing Group Stephan Holzer Deterministic Multi-Channel Information Exchange n:= # nodes k:= # information Range of k[log n, n] Upper bound On channels 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 bound On channels 1 This paper: randomized deterministic](http://images.slideplayer.com./47/11690858/slides/slide_20.jpg "ETH Zurich – Distributed Computing Group Stephan Holzer Deterministic Multi-Channel Information Exchange n:= # nodes k:= # information Range of k[log n, n] Upper bound On channels 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 bound On channels 1 This paper: randomized deterministic")
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ETH Zurich – Distributed Computing Group Stephan Holzer Deterministic Multi-Channel Information Exchange n:= # nodes k:= # information Range of k[log n, n] Upper bound On channels 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 bound On channels 1 This paper: randomized deterministic Optimal?
![ETH Zurich – Distributed Computing Group Stephan Holzer Deterministic Multi-Channel Information Exchange n:= # nodes k:= # information Range of k[log n, n] Upper bound On channels 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 bound On channels 1 This paper: randomized deterministic Optimal](http://images.slideplayer.com./47/11690858/slides/slide_21.jpg "ETH Zurich – Distributed Computing Group Stephan Holzer Deterministic Multi-Channel Information Exchange n:= # nodes k:= # information Range of k[log n, n] Upper bound On channels 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 bound On channels 1 This paper: randomized deterministic Optimal")
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ETH Zurich – Distributed Computing Group Stephan Holzer Deterministic Multi-Channel Information Exchange n:= # nodes k:= # information Range of k[log n, n] Upper bound On channels 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 bound On channels 1 Lower bound On channels 1 This paper: randomized deterministic k
![ETH Zurich – Distributed Computing Group Stephan Holzer Deterministic Multi-Channel Information Exchange n:= # nodes k:= # information Range of k[log n, n] Upper bound On channels 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 bound On channels 1 Lower bound On channels 1 This paper: randomized deterministic k](http://images.slideplayer.com./47/11690858/slides/slide_22.jpg "ETH Zurich – Distributed Computing Group Stephan Holzer Deterministic Multi-Channel Information Exchange n:= # nodes k:= # information Range of k[log n, n] Upper bound On channels 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 bound On channels 1 Lower bound On channels 1 This paper: randomized deterministic k")
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ETH Zurich – Distributed Computing Group Stephan Holzer Deterministic Multi-Channel Information Exchange Main ingredient: Specially taylored graphs.
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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])
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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.
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ETH Zurich – Distributed Computing Group Stephan Holzer Deterministic Multi-Channel Information Exchange 7 6 5 4 3 2 1 Bipartite : node IDs new names
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ETH Zurich – Distributed Computing Group Stephan Holzer Deterministic Multi-Channel Information Exchange 7 6 5 4 3 2 1 Bipartite : node IDs new names
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ETH Zurich – Distributed Computing Group Stephan Holzer Deterministic Multi-Channel Information Exchange
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ETH Zurich – Distributed Computing Group Stephan Holzer Deterministic Multi-Channel Information Exchange
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ETH Zurich – Distributed Computing Group Stephan Holzer Deterministic Multi-Channel Information Exchange
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ETH Zurich – Distributed Computing Group Stephan Holzer Deterministic Multi-Channel Information Exchange 7 6 5 4 3 2 1 i i have unique i-neighbor
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ETH Zurich – Distributed Computing Group Stephan Holzer Deterministic Multi-Channel Information Exchange 7 6 5 4 3 2 1 i i have unique i-neighbor
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ETH Zurich – Distributed Computing Group Stephan Holzer Deterministic Multi-Channel Information Exchange 7 6 5 4 3 2 1 1 1 1 2 1 2 2 2
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ETH Zurich – Distributed Computing Group Stephan Holzer Deterministic Multi-Channel Information Exchange 7 6 5 4 3 2 1 1 1 1 2 1 2 2 2 X
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ETH Zurich – Distributed Computing Group Stephan Holzer Deterministic Multi-Channel Information Exchange 7 6 5 4 3 2 1 1 1 1 1 X
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ETH Zurich – Distributed Computing Group Stephan Holzer Deterministic Multi-Channel Information Exchange 7 6 5 4 3 2 1 1 1 1 1 X BAD
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ETH Zurich – Distributed Computing Group Stephan Holzer Deterministic Multi-Channel Information Exchange 7 6 5 4 3 2 1 1 1 1 2 1 2 2 2 X
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ETH Zurich – Distributed Computing Group Stephan Holzer Deterministic Multi-Channel Information Exchange 7 6 5 4 3 2 1 2 2 2 2 X
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ETH Zurich – Distributed Computing Group Stephan Holzer Deterministic Multi-Channel Information Exchange 7 6 5 4 3 2 1 2 2 2 2 X GOOD
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ETH Zurich – Distributed Computing Group Stephan Holzer Deterministic Multi-Channel Information Exchange 7 6 5 4 3 2 1 1 1 1 1 X
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ETH Zurich – Distributed Computing Group Stephan Holzer Deterministic Multi-Channel Information Exchange 7 6 5 4 3 2 1 1 1 1 1 X
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ETH Zurich – Distributed Computing Group Stephan Holzer Deterministic Multi-Channel Information Exchange 7 6 5 4 3 2 1 1 1 1 2 1 2 2 2
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ETH Zurich – Distributed Computing Group Stephan Holzer Deterministic Multi-Channel Information Exchange What are these graphs good for?
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ETH Zurich – Distributed Computing Group Stephan Holzer Deterministic Multi-Channel Information Exchange What are these graphs good for? Renaming
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ETH Zurich – Distributed Computing Group Stephan Holzer Deterministic Multi-Channel Information Exchange What are these graphs good for? Renaming 7 6 5 4 3 2 1 1 1 1 2 1 2 2 2
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ETH Zurich – Distributed Computing Group Stephan Holzer Deterministic Multi-Channel Information Exchange 7 6 5 4 3 2 1 1 1 1 2 1 2 2 2
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ETH Zurich – Distributed Computing Group Stephan Holzer Deterministic Multi-Channel Information Exchange What is renaming good for?
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ETH Zurich – Distributed Computing Group Stephan Holzer Deterministic Multi-Channel Information Exchange What is renaming good for? Assignment of reporters to channels!
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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
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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
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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 New names of reporters
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ETH Zurich – Distributed Computing Group Stephan Holzer Deterministic Multi-Channel Information Exchange n Original names New names of reporters
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ETH Zurich – Distributed Computing Group Stephan Holzer Deterministic Multi-Channel Information Exchange n:= # nodes k:= # information n Original names New names of reporters
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ETH Zurich – Distributed Computing Group Stephan Holzer Deterministic Multi-Channel Information Exchange n:= # nodes k:= # information Time: O( k ) n Original names New names of reporters
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ETH Zurich – Distributed Computing Group Stephan Holzer Deterministic Multi-Channel Information Exchange n:= # nodes k:= # information n Original names New names of reporters
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ETH Zurich – Distributed Computing Group Stephan Holzer Deterministic Multi-Channel Information Exchange n:= # nodes k:= # information n Original names New names of reporters
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ETH Zurich – Distributed Computing Group Stephan Holzer Deterministic Multi-Channel Information Exchange n:= # nodes k:= # information n Original names New names of reporters
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ETH Zurich – Distributed Computing Group Stephan Holzer Deterministic Multi-Channel Information Exchange n:= # nodes k:= # information n Original names New names of reporters
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ETH Zurich – Distributed Computing Group Stephan Holzer Deterministic Multi-Channel Information Exchange n:= # nodes k:= # information
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ETH Zurich – Distributed Computing Group Stephan Holzer Deterministic Multi-Channel Information Exchange n:= # nodes k:= # information Example: 3 channels
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ETH Zurich – Distributed Computing Group Stephan Holzer Deterministic Multi-Channel Information Exchange n:= # nodes k:= # information Channel 3 Example: 3 channels Channel 1
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ETH Zurich – Distributed Computing Group Stephan Holzer Deterministic Multi-Channel Information Exchange n:= # nodes k:= # information Channel 3 Example: 3 channels Channel 1 Send 2 times
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ETH Zurich – Distributed Computing Group Stephan Holzer Deterministic Multi-Channel Information Exchange n:= # nodes k:= # information Channel 3 Example: 3 channels Channel 1 Send 2 times
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ETH Zurich – Distributed Computing Group Stephan Holzer Deterministic Multi-Channel Information Exchange n:= # nodes k:= # information Channel 3 Example: 3 channels Channel 1 Send 2 times
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ETH Zurich – Distributed Computing Group Stephan Holzer Deterministic Multi-Channel Information Exchange n:= # nodes k:= # information Channel 3 Example: 3 channels Channel 1 Send 2 times
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ETH Zurich – Distributed Computing Group Stephan Holzer Deterministic Multi-Channel Information Exchange n:= # nodes k:= # information Unique Subset Channel 3 Example: 3 channels Channel 1 Send 2 times
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ETH Zurich – Distributed Computing Group Stephan Holzer Deterministic Multi-Channel Information Exchange n:= # nodes k:= # information Unique Subset Channel 3 Example: 3 channels Channel 1 Send 2 times
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ETH Zurich – Distributed Computing Group Stephan Holzer Deterministic Multi-Channel Information Exchange n:= # nodes k:= # information Unique Subset Channel 3 Example: 3 channels Channel 1 Send 2 times
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ETH Zurich – Distributed Computing Group Stephan Holzer Deterministic Multi-Channel Information Exchange Unique Subset Channel 3 Example: 3 channels Channel 1 Send k times O( k ) n:= # nodes k:= # information
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ETH Zurich – Distributed Computing Group Stephan Holzer Deterministic Multi-Channel Information Exchange 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 bound On channels 1 Lower bound On channels 1
 [log n loglog n, n- log n) [n – log n, n] Upper bound On channels 1 Lower bound On channels 1](http://images.slideplayer.com./47/11690858/slides/slide_70.jpg "ETH Zurich – Distributed Computing Group Stephan Holzer Deterministic Multi-Channel Information Exchange 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 bound On channels 1 Lower bound On channels 1")
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ETH Zurich – Distributed Computing Group Stephan Holzer Deterministic Multi-Channel Information Exchange n Original names New names of reporters
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ETH Zurich – Distributed Computing Group Stephan Holzer Deterministic Multi-Channel Information Exchange in Summary … Detect / Disseminate Information! 101 Mhz 117 Mhz 132 Mhz … 7 6 5 4 3 2 1 1 1 1 2 1 2 2 2 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 bound On channels 1 Lower bound On channels 1
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ETH Zurich – Distributed Computing Group Stephan HolzerETH Zurich – Distributed Computing – www.disco.ethz.ch Stephan Holzer - ETH Zürich Thomas Locher - ABB Switzerland Yvonne Anne Pignolet - ABB Switzerland Roger Wattenhofer - ETH Zürich Thank You! Questions & Comments? TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAA A A A
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ETH Zurich – Distributed Computing Group Stephan HolzerETH Zurich – Distributed Computing – www.disco.ethz.ch Stephan Holzer - ETH Zürich Thomas Locher - ABB Switzerland Yvonne Anne Pignolet - ABB Switzerland Roger Wattenhofer - ETH Zürich Thank You! Questions & Comments? TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAA A A A
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