Deterministic MultiChannel Information Exchange Stephan Holzer ETH Zrich

Deterministic Multi-Channel Information Exchange Stephan Holzer - ETH Zürich Thomas Locher - ABB Switzerland Yvonne Anne Pignolet - ABB Switzerland Roger Wattenhofer - ETH Zürich ETH Zurich – Distributed Computing –Group www. disco. ethz. ch 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 n: = # nodes Problem: 1 5 2 3 Unique IDs 1…n 4 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 node ETH Zurich – Distributed Computing Group Stephan Holzer

Deterministic Multi-Channel Information Exchange I can: send / receive reach node ETH Zurich – Distributed Computing Group Stephan Holzer ?

Deterministic Multi-Channel Information Exchange I can: send / receive reach node no collision detection ETH Zurich – Distributed Computing Group Stephan Holzer

Deterministic Multi-Channel Information Exchange I can: send / receive reach node no collision detection switch channels ETH Zurich – Distributed Computing Group 101 Mhz 117 Mhz 132 Mhz … synchronus Stephan Holzer

Deterministic Multi-Channel Information Exchange I can: send / receive reach node complexity computation: free radio: time 1 no collision detection switch channels synchronus ETH Zurich – Distributed Computing Group Stephan Holzer

Deterministic Multi-Channel Information Exchange n: = # nodes k: = # information [GW 85]: Time Channels Ω(k + log n) 1 k ETH Zurich – Distributed Computing Group Stephan Holzer

Deterministic Multi-Channel Information Exchange n: = # nodes k: = # information [GW 85]: [HPSW 11]: Time Channels k Ω(k + log n) 1 k O(k) n ETH Zurich – Distributed Computing Group Stephan Holzer

Deterministic Multi-Channel Information Exchange n: = # nodes k: = # information [GW 85]: [HPSW 11]: Time Channels k Ω(k + log n) 1 k O(k) n l a m i t p O ETH Zurich – Distributed Computing Group Stephan Holzer

Deterministic Multi-Channel Information Exchange n: = # nodes k: = # information [GW 85]: [HPSW 11]: Time Channels k Ω(k + log n) 1 k O(k) n l a m i t p O ETH Zurich – Distributed Computing Group ? ? ? ? Stephan Holzer

Deterministic Multi-Channel Information Exchange n: = # nodes k: = # information [HPSW 11] - Channels needed for time O(k): Range of k [log n , n] Upper bound On channels ETH Zurich – Distributed Computing Group 1 Stephan Holzer

Deterministic Multi-Channel Information Exchange n: = # nodes k: = # information [HPSW 11] - Channels needed for time O(k): Range of k [log n , n] Upper bound On channels 1 This paper: Range of k [1, log n] (log n , log n loglog n) Upper bound On channels ETH Zurich – Distributed Computing Group [log n loglog n , [n – log n, n] n- log n) 1 Stephan Holzer

Deterministic Multi-Channel Information Exchange n: = # nodes k: = # information [HPSW 11] - Channels needed for time O(k): randomized Range of k [log n , n] Upper bound On channels 1 This paper: Range of k [1, log n] (log n , log n loglog n) Upper bound On channels ETH Zurich – Distributed Computing Group [log n loglog n , [n – log n, n] n- log n) 1 Stephan Holzer

Deterministic Multi-Channel Information Exchange n: = # nodes k: = # information [HPSW 11] - Channels needed for time O(k): randomized Range of k [log n , n] Upper bound On channels 1 This paper: deterministic Range of k [1, log n] (log n , log n loglog n) Upper bound On channels ETH Zurich – Distributed Computing Group [log n loglog n , [n – log n, n] n- log n) 1 Stephan Holzer

Deterministic Multi-Channel Information Exchange n: = # nodes k: = # information [HPSW 11] - Channels needed for time O(k): randomized Range of k [log n , n] Upper bound On channels 1 This paper: deterministic Range of k [1, log n] (log n , log n loglog n) [log n loglog n , [n – log n, n] n- log n) Upper bound On channels ? l a m ti p O 1 ? l a O m i t p ETH Zurich – Distributed Computing Group ? l a m i t p Stephan Holzer m i t p ? l a

Deterministic Multi-Channel Information Exchange n: = # nodes k: = # information [HPSW 11] - Channels needed for time O(k): randomized Range of k [log n , n] Upper bound On channels 1 This paper: deterministic Range of k [1, log n] (log n , log n loglog n) [log n loglog n , [n – log n, n] n- log n) Upper bound On channels 1 Lower bound On channels ETH Zurich – Distributed Computing Group k Stephan Holzer 1

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 [CK 08]) ETH Zurich – Distributed Computing Group Stephan Holzer

Deterministic Multi-Channel Information Exchange Main ingredient: Specially taylored graphs. (Inspired by use of lossless expanders in [CK 08]) 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 1 5 2 6 3 7 4 ETH Zurich – Distributed Computing Group Stephan Holzer

Deterministic Multi-Channel Information Exchange Bipartite : node IDs new names 1 5 2 6 3 7 4 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 • 1 5 2 have unique i-neighbor ETH Zurich – Distributed Computing Group Stephan Holzer 3 4 i 6 i 7

Deterministic Multi-Channel Information Exchange • 1 5 2 have unique i-neighbor ETH Zurich – Distributed Computing Group Stephan Holzer 3 4 i 6 i 7

Deterministic Multi-Channel Information Exchange • 1 1 2 2 2 1 2 3 1 2 4 1 ETH Zurich – Distributed Computing Group Stephan Holzer 5 6 7

Deterministic Multi-Channel Information Exchange • X ETH Zurich – Distributed Computing Group Stephan Holzer 1 1 2 2 2 1 2 3 1 2 4 1 5 6 7

Deterministic Multi-Channel Information Exchange • 1 1 2 3 X ETH Zurich – Distributed Computing Group Stephan Holzer 5 1 6 1 4 1 7

Deterministic Multi-Channel Information Exchange • 1 1 2 3 X ETH Zurich – Distributed Computing Group Stephan Holzer 5 1 6 1 4 1 7 BAD

Deterministic Multi-Channel Information Exchange • X ETH Zurich – Distributed Computing Group Stephan Holzer 1 1 2 2 2 1 2 3 1 2 4 1 5 6 7

Deterministic Multi-Channel Information Exchange • 1 2 3 X ETH Zurich – Distributed Computing Group Stephan Holzer 4 2 2 5 2 6 2 7

Deterministic Multi-Channel Information Exchange • 1 2 3 X ETH Zurich – Distributed Computing Group Stephan Holzer 4 2 2 5 2 6 2 7 GOOD

Deterministic Multi-Channel Information Exchange • X 1 1 2 3 5 1 1 4 1 ETH Zurich – Distributed Computing Group Stephan Holzer 6 7

Deterministic Multi-Channel Information Exchange • X 1 1 2 3 5 1 1 4 1 ETH Zurich – Distributed Computing Group Stephan Holzer 6 7

Deterministic Multi-Channel Information Exchange • 1 1 2 2 2 1 2 3 1 2 4 1 ETH Zurich – Distributed Computing Group Stephan Holzer 5 6 7

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 1 1 2 2 2 1 2 3 1 2 4 1 5 6 7

Deterministic Multi-Channel Information Exchange • 1 1 2 2 2 1 2 3 1 2 4 1 ETH Zurich – Distributed Computing Group Stephan Holzer 5 6 7

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 Original names 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 Original names n ETH Zurich – Distributed Computing Group New names of reporters Stephan Holzer

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

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

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

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

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

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

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

Deterministic Multi-Channel Information Exchange n: = # nodes k: = # information Example: 3 channels Send 2 times Channel 1 ETH Zurich – Distributed Computing Group Channel 3 Stephan Holzer

Deterministic Multi-Channel Information Exchange n: = # nodes k: = # information Example: 3 channels Send 2 times Channel 1 ETH Zurich – Distributed Computing Group Channel 3 Stephan Holzer

Deterministic Multi-Channel Information Exchange n: = # nodes k: = # information Example: 3 channels Send 2 times Channel 1 ETH Zurich – Distributed Computing Group Channel 3 Stephan Holzer

Deterministic Multi-Channel Information Exchange n: = # nodes k: = # information Example: 3 channels Send 2 times Channel 1 ETH Zurich – Distributed Computing Group Channel 3 Stephan Holzer

Deterministic Multi-Channel Information Exchange n: = # nodes k: = # information Example: 3 channels Unique Subset Send 2 times Channel 1 ETH Zurich – Distributed Computing Group Channel 3 Stephan Holzer

Deterministic Multi-Channel Information Exchange n: = # nodes k: = # information Example: 3 channels Unique Subset Send 2 times Channel 1 ETH Zurich – Distributed Computing Group Channel 3 Stephan Holzer

Deterministic Multi-Channel Information Exchange n: = # nodes k: = # information Example: 3 channels Unique Subset Send 2 times Channel 1 ETH Zurich – Distributed Computing Group Channel 3 Stephan Holzer

Deterministic Multi-Channel Information Exchange n: = # nodes k: = # information Example: 3 channels O( k ) Send k times Channel 1 ETH Zurich – Distributed Computing Group Unique Subset Channel 3 Stephan Holzer

Deterministic Multi-Channel Range of k [1, log n] (log n , Information Exchange log n loglog n) [log n loglog n , [n – log n, n] n- log n) Upper bound On channels 1 Lower bound On channels 1 O( k ) ETH Zurich – Distributed Computing Group Stephan Holzer

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

Deterministic Multi-Channel Information Exchange in Summary … Detect / Disseminate Information! 101 Mhz 117 Mhz 132 Mhz … Range of k [1, log n] X (log n , log n loglog n) 1 1 2 2 2 1 3 2 1 4 2 1 5 6 7 [log n loglog n , [n – log n, n] n- log n) Upper bound On channels 1 Lower bound On channels 1 ETH Zurich – Distributed Computing Group Stephan Holzer

Thank You! Questions & Comments? Stephan Holzer - ETH Zürich Thomas Locher - ABB Switzerland Yvonne Anne Pignolet - ABB Switzerland Roger Wattenhofer - ETH Zürich ETH Zurich – Distributed Computing –Group www. disco. ethz. ch Stephan Holzer

Thank You! Questions & Comments? Stephan Holzer - ETH Zürich Thomas Locher - ABB Switzerland Yvonne Anne Pignolet - ABB Switzerland Roger Wattenhofer - ETH Zürich ETH Zurich – Distributed Computing –Group www. disco. ethz. ch Stephan Holzer