1. ETH Zurich – Distributed Computing Group Stephan Holzer 1ETH Zurich – Distributed Computing – www.disco.ethz.ch Stephan Holzer Yvonne Anne Pignolet Jasmin Smula Roger Wattenhofer TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAA A A AA AA Time-Optimal Information Exchange on Multiple Channels

2. ETH Zurich – Distributed Computing Group Stephan Holzer 2 Problem : Time-Optimal Information Exchange on Multiple Channels n:= # nodes

3. ETH Zurich – Distributed Computing Group Stephan Holzer 3 Problem : Time-Optimal Information Exchange on Multiple Channels n:= # nodes k:= # information Have information Disseminate to all! ?

4. ETH Zurich – Distributed Computing Group Stephan Holzer 4 Problem : Time-Optimal Information Exchange on Multiple Channels Disseminate to all! ?

5. ETH Zurich – Distributed Computing Group Stephan Holzer 5 Problem : Time-Optimal Information Exchange on Multiple Channels Disseminate to all! ? Easy: O(n) Faster?

6. ETH Zurich – Distributed Computing Group Stephan Holzer 6 Problem : Time-Optimal Information Exchange on Multiple Channels n:= # nodes 1 2 3 4 5 n Unique IDs 1…n

7. ETH Zurich – Distributed Computing Group Stephan Holzer 7 I can: send / receive reach each node Time-Optimal Information Exchange on Multiple Channels

8. ETH Zurich – Distributed Computing Group Stephan Holzer 8 I can: send / receive ? reach each node Time-Optimal Information Exchange on Multiple Channels

9. ETH Zurich – Distributed Computing Group Stephan Holzer 9 Time-Optimal Information Exchange on Multiple Channels no collision detection I can: send / receive reach each node

10. ETH Zurich – Distributed Computing Group Stephan Holzer 10 switch channels no collision detection I can: send / receive reach each node 101 Mhz 117 Mhz 132 Mhz … Time-Optimal Information Exchange on Multiple Channels

11. ETH Zurich – Distributed Computing Group Stephan Holzer 11 switch channels no collision detection I can: send / receive reach each node complexity computation: free radio: time 1 Time-Optimal Information Exchange on Multiple Channels

12. ETH Zurich – Distributed Computing Group Stephan Holzer 12 One Information / log n bits per message O(1) Time-Optimal Information Exchange on Multiple Channels n:= # nodes k:= # information => Ω( k )

13. ETH Zurich – Distributed Computing Group Stephan Holzer 13 => Ω( k ) Time-Optimal Information Exchange on Multiple Channels n:= # nodes k:= # information + log n [Kushilevitz, Mansour SIAM JComp 1998] one channel ? Multi channel

14. ETH Zurich – Distributed Computing Group Stephan Holzer 14 Problem : Time-Optimal Information Exchange on Multiple Channels How to find them In time O(2) ?

15. ETH Zurich – Distributed Computing Group Stephan Holzer 15ETH Zurich – Distributed Computing – www.disco.ethz.ch Stephan Holzer Yvonne Anne Pignolet Jasmin Smula Roger Wattenhofer Thank You! Questions & Comments? TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAA A A A