ETH Zurich Distributed Computing Group Stephan Holzer 1ETH Zurich Distributed Computing 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 ETH Zurich Distributed Computing Group Stephan Holzer 2 Problem : Time-Optimal Information Exchange on Multiple Channels n:= # nodes 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! ? ETH Zurich Distributed Computing Group Stephan Holzer 4 Problem : Time-Optimal Information Exchange on Multiple Channels Disseminate to all! ? ETH Zurich Distributed Computing Group Stephan Holzer 5 Problem : Time-Optimal Information Exchange on Multiple Channels Disseminate to all! ? Easy: O(n) Faster? ETH Zurich Distributed Computing Group Stephan Holzer 6 Problem : Time-Optimal Information Exchange on Multiple Channels n:= # nodes n Unique IDs 1n ETH Zurich Distributed Computing Group Stephan Holzer 7 I can: send / receive reach each node Time-Optimal Information Exchange on Multiple Channels ETH Zurich Distributed Computing Group Stephan Holzer 8 I can: send / receive ? reach each node Time-Optimal Information Exchange on Multiple Channels 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 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 synchronus 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 synchronus 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 => ( k ) ETH Zurich Distributed Computing Group Stephan Holzer 13 => ( k ) Time-Optimal Information Exchange on Multiple Channels n:= # nodes k:= # information + log n [Kushilevitz, Mansour SIAM JComp 1998] one channel ? Multi channel ETH Zurich Distributed Computing Group Stephan Holzer 14 Time-Optimal Information Exchange on Multiple Channels n:= # nodes k:= # information TREE What can I do? ETH Zurich Distributed Computing Group Stephan Holzer Time-Optimal Information Exchange on Multiple Channels n:= # nodes k:= # information TREE Communicate in parallel on different channels ETH Zurich Distributed Computing Group Stephan Holzer Time-Optimal Information Exchange on Multiple Channels n:= # nodes k:= # information TREE Communicate in parallel on different channels ETH Zurich Distributed Computing Group Stephan Holzer 17 Time-Optimal Information Exchange on Multiple Channels n:= # nodes k:= # information TREE ETH Zurich Distributed Computing Group Stephan Holzer 18 Time-Optimal Information Exchange on Multiple Channels n:= # nodes k:= # information TREE ETH Zurich Distributed Computing Group Stephan Holzer 19 Time-Optimal Information Exchange on Multiple Channels n:= # nodes k:= # information TREE ETH Zurich Distributed Computing Group Stephan Holzer 20 Time-Optimal Information Exchange on Multiple Channels n:= # nodes k:= # information TREE ETH Zurich Distributed Computing Group Stephan Holzer 21 Time-Optimal Information Exchange on Multiple Channels n:= # nodes k:= # information TREE ETH Zurich Distributed Computing Group Stephan Holzer 22 TREE Time-Optimal Information Exchange on Multiple Channels n:= # nodes k:= # information O( k + log n) ETH Zurich Distributed Computing Group Stephan Holzer 23 Time-Optimal Information Exchange on Multiple Channels What if k < log n? n:= # nodes k:= # information O( k ) if k > log n n channels TREE ETH Zurich Distributed Computing Group Stephan Holzer 24 Time-Optimal Information Exchange on Multiple Channels What if k < log n? n:= # nodes k:= # information ETH Zurich Distributed Computing Group Stephan Holzer 25 Time-Optimal Information Exchange on Multiple Channels n:= # nodes k:= # information Assume: k known ETH Zurich Distributed Computing Group Stephan Holzer 26 Time-Optimal Information Exchange on Multiple Channels n:= # nodes k:= # information Assume: k known Balls into Bins ETH Zurich Distributed Computing Group Stephan Holzer 27 Time-Optimal Information Exchange on Multiple Channels n:= # nodes k:= # information Assume: k known Balls into Bins ID=12 k ETH Zurich Distributed Computing Group Stephan Holzer 28 Time-Optimal Information Exchange on Multiple Channels n:= # nodes k:= # information Assume: k known Balls into Bins ID=12 k ETH Zurich Distributed Computing Group Stephan Holzer 29 Time-Optimal Information Exchange on Multiple Channels n:= # nodes k:= # information Assume: k known Balls into Bins Listens on channel 1 Listens on channel 2 Listens on channel 3 Listens on channel 4 Send on random channel 12 ID=12 k k ETH Zurich Distributed Computing Group Stephan Holzer 30 Time-Optimal Information Exchange on Multiple Channels n:= # nodes k:= # information Assume: k known Balls into Bins Listens on channel 1 Listens on channel 2 Listens on channel 3 Listens on channel 4 ID=12 k Send on random channel 12 k ETH Zurich Distributed Computing Group Stephan Holzer 31 Time-Optimal Information Exchange on Multiple Channels n:= # nodes k:= # information Assume: k known Balls into Bins Pr no collision ID=12 k ETH Zurich Distributed Computing Group Stephan Holzer 32 Time-Optimal Information Exchange on Multiple Channels n:= # nodes k:= # information Assume: k known ID=12 k Balls into Bins Pr no collision TREE ETH Zurich Distributed Computing Group Stephan Holzer 33 Time-Optimal Information Exchange on Multiple Channels n:= # nodes k:= # information Assume: k known ID=12 k Balls into Bins Pr no collision TREE ETH Zurich Distributed Computing Group Stephan Holzer 34 Time-Optimal Information Exchange on Multiple Channels n:= # nodes k:= # information Assume: k known ID=12 k Balls into Bins Pr no collision Repeat k times ETH Zurich Distributed Computing Group Stephan Holzer 35 Time-Optimal Information Exchange on Multiple Channels n:= # nodes k:= # information Assume: k known ID=12 k Balls into Bins TREE Repeat k times k 2 channels ETH Zurich Distributed Computing Group Stephan Holzer 36 Time-Optimal Information Exchange on Multiple Channels n:= # nodes k:= # information Assume: k known Unique Subset Time: O( k ) ETH Zurich Distributed Computing Group Stephan Holzer 37 Time-Optimal Information Exchange on Multiple Channels n:= # nodes k:= # information Assume: k known Unique Subset ETH Zurich Distributed Computing Group Stephan Holzer 38 Time-Optimal Information Exchange on Multiple Channels n:= # nodes k:= # information Assume: k known Unique Subset ETH Zurich Distributed Computing Group Stephan Holzer 39 Time-Optimal Information Exchange on Multiple Channels n:= # nodes k:= # information Assume: k known Unique Subset ETH Zurich Distributed Computing Group Stephan Holzer 40 Time-Optimal Information Exchange on Multiple Channels n:= # nodes k:= # information Assume: k known Unique Subset ETH Zurich Distributed Computing Group Stephan Holzer 41 Time-Optimal Information Exchange on Multiple Channels n:= # nodes k:= # information Assume: k known Unique Subset Not too big Not too small Just right! ETH Zurich Distributed Computing Group Stephan Holzer 42 Time-Optimal Information Exchange on Multiple Channels n:= # nodes k:= # information Assume: k known Unique Subset Channel 3 Example: 3 channels Channel 1 ETH Zurich Distributed Computing Group Stephan Holzer 43 Time-Optimal Information Exchange on Multiple Channels n:= # nodes k:= # information Assume: k known Unique Subset Channel 3 Example: 3 channels Channel 1 Send k times ETH Zurich Distributed Computing Group Stephan Holzer 44 Time-Optimal Information Exchange on Multiple Channels n:= # nodes k:= # information Assume: k known Unique Subset Channel 3 Example: 3 channels Channel 1 Send k times ETH Zurich Distributed Computing Group Stephan Holzer 45 Time-Optimal Information Exchange on Multiple Channels n:= # nodes k:= # information Assume: k known Unique Subset Channel 3 Example: 3 channels Channel 1 Send k times ETH Zurich Distributed Computing Group Stephan Holzer 46 Time-Optimal Information Exchange on Multiple Channels n:= # nodes k:= # information Assume: k known Unique Subset Channel 3 Example: 3 channels Channel 1 ? ? ? Send k times ETH Zurich Distributed Computing Group Stephan Holzer 47 Time-Optimal Information Exchange on Multiple Channels n:= # nodes k:= # information Assume: k known Unique Subset Channel 3 Example: 3 channels Channel 1 Send k times ETH Zurich Distributed Computing Group Stephan Holzer 48 Time-Optimal Information Exchange on Multiple Channels n:= # nodes k:= # information Assume: k known Unique Subset Channel 3 Example: 3 channels Channel 1 Send k times ETH Zurich Distributed Computing Group Stephan Holzer 49 Time-Optimal Information Exchange on Multiple Channels n:= # nodes k:= # information Assume: k known Unique Subset Channel 3 Example: 3 channels Channel 1 Send k times ETH Zurich Distributed Computing Group Stephan Holzer 50 Time-Optimal Information Exchange on Multiple Channels n:= # nodes k:= # information Assume: k known Unique Subset Example: 3 channels O( k ) ETH Zurich Distributed Computing Group Stephan Holzer 51 Time-Optimal Information Exchange on Multiple Channels n:= # nodes k:= # information Assume: k known Unique Subset Example: 3 channels O( k + k/2 + k/4 ETH Zurich Distributed Computing Group Stephan Holzer 52 Time-Optimal Information Exchange on Multiple Channels n:= # nodes k:= # information Assume: k known Unique Subset Example: 3 channels O( k ) ETH Zurich Distributed Computing Group Stephan Holzer 53 Time-Optimal Information Exchange on Multiple Channels n:= # nodes k:= # information Assume: k known Unique Subset Balls into Bins TREE ETH Zurich Distributed Computing Group Stephan Holzer 54 Time-Optimal Information Exchange on Multiple Channels n:= # nodes k:= # information Assume: k known unknown Unique Subset Balls into Bins TREE n channels 2 channels k n channels Future directions:deterministic less channels lower bounds ETH Zurich Distributed Computing Group Stephan Holzer 55 in Summary Detect / Disseminate Information! Time-Optimal Information Exchange on Multiple Channels 101 Mhz 117 Mhz 132 Mhz ETH Zurich Distributed Computing Group Stephan Holzer 56ETH Zurich Distributed Computing 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