ETH Zurich – Distributed Computing Group Stephan HolzerETH Zurich – Distributed Computing – Stephan Holzer - ETH Zürich Thomas Locher.

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Presentation transcript:

ETH Zurich – Distributed Computing Group Stephan HolzerETH Zurich – Distributed Computing – 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

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:= # nodes k:= # 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 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 Exchange I can: send / receive reach each node

ETH Zurich – Distributed Computing Group Stephan Holzer Deterministic Multi-Channel Information Exchange I 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 Mhz 117 Mhz 132 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 complexity computation: free radio: time 1 synchronus

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 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 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

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): 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: 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 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 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 Lower bound On channels 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 Bipartite : node IDs new names

ETH Zurich – Distributed Computing Group Stephan Holzer Deterministic Multi-Channel Information Exchange Bipartite : node IDs new names

ETH Zurich – Distributed Computing Group Stephan Holzer Deterministic Multi-Channel Information Exchange

ETH Zurich – Distributed Computing Group Stephan Holzer Deterministic Multi-Channel Information Exchange

ETH Zurich – Distributed Computing Group Stephan Holzer Deterministic Multi-Channel Information Exchange

ETH Zurich – Distributed Computing Group Stephan Holzer Deterministic Multi-Channel Information Exchange i i have unique i-neighbor

ETH Zurich – Distributed Computing Group Stephan Holzer Deterministic Multi-Channel Information Exchange i i have unique i-neighbor

ETH Zurich – Distributed Computing Group Stephan Holzer Deterministic Multi-Channel Information Exchange

ETH Zurich – Distributed Computing Group Stephan Holzer Deterministic Multi-Channel Information Exchange X

ETH Zurich – Distributed Computing Group Stephan Holzer Deterministic Multi-Channel Information Exchange X

ETH Zurich – Distributed Computing Group Stephan Holzer Deterministic Multi-Channel Information Exchange X BAD

ETH Zurich – Distributed Computing Group Stephan Holzer Deterministic Multi-Channel Information Exchange X

ETH Zurich – Distributed Computing Group Stephan Holzer Deterministic Multi-Channel Information Exchange X

ETH Zurich – Distributed Computing Group Stephan Holzer Deterministic Multi-Channel Information Exchange X GOOD

ETH Zurich – Distributed Computing Group Stephan Holzer Deterministic Multi-Channel Information Exchange X

ETH Zurich – Distributed Computing Group Stephan Holzer Deterministic Multi-Channel Information Exchange X

ETH Zurich – Distributed Computing Group Stephan Holzer Deterministic Multi-Channel Information Exchange

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

ETH Zurich – Distributed Computing Group Stephan Holzer Deterministic Multi-Channel Information Exchange

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 New names of reporters

ETH Zurich – Distributed Computing Group Stephan Holzer Deterministic Multi-Channel Information Exchange n Original names New names of reporters

ETH Zurich – Distributed Computing Group Stephan Holzer Deterministic Multi-Channel Information Exchange n:= # nodes k:= # information n Original names New names of reporters

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

ETH Zurich – Distributed Computing Group Stephan Holzer Deterministic Multi-Channel Information Exchange n:= # nodes k:= # information n Original names New names of reporters

ETH Zurich – Distributed Computing Group Stephan Holzer Deterministic Multi-Channel Information Exchange n:= # nodes k:= # information n Original names New names of reporters

ETH Zurich – Distributed Computing Group Stephan Holzer Deterministic Multi-Channel Information Exchange n:= # nodes k:= # information n Original names New names of reporters

ETH Zurich – Distributed Computing Group Stephan Holzer Deterministic Multi-Channel Information Exchange n:= # nodes k:= # information n Original names New names of reporters

ETH Zurich – Distributed Computing Group Stephan Holzer Deterministic Multi-Channel Information Exchange n:= # nodes k:= # information

ETH Zurich – Distributed Computing Group Stephan Holzer Deterministic Multi-Channel Information Exchange n:= # nodes k:= # information Example: 3 channels

ETH Zurich – Distributed Computing Group Stephan Holzer Deterministic Multi-Channel Information Exchange n:= # nodes k:= # information Channel 3 Example: 3 channels Channel 1

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

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

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

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

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

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

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

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

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

ETH Zurich – Distributed Computing Group Stephan Holzer Deterministic Multi-Channel Information Exchange n Original names New names of reporters

ETH Zurich – Distributed Computing Group Stephan Holzer Deterministic Multi-Channel Information Exchange in Summary … Detect / Disseminate Information! 101 Mhz 117 Mhz 132 Mhz … 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

ETH Zurich – Distributed Computing Group Stephan HolzerETH Zurich – Distributed Computing – 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

ETH Zurich – Distributed Computing Group Stephan HolzerETH Zurich – Distributed Computing – 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