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Let’s get Physical!

This talk provides an introduction to physical algorithms and explores the topic of clock synchronization in distributed computing. It covers various examples of physical algorithms, discusses the challenges and solutions in clock synchronization, and explores the implications and future of computing.

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Let’s get Physical!

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  1. Let’s get Physical! ETH Zurich –Distributed Computing –www.disco.ethz.ch ICALP 2010 – Roger Wattenhofer

  2. Spot the Differences

  3. TooMany!

  4. Spot the Differences

  5. Still Many!

  6. Spot the Differences

  7. Better ScreenBigger DiskMore RAMCooler Design…

  8. Better ScreenBigger DiskMore RAMCooler Design…Same CPU Clock Speed

  9. Transistor count still rising Clock speed flattening sharply Advent of multi-core processors!

  10. The Future of Computing

  11. WhyShould I Care?

  12. Computer Science  Washing Machine Science [Roger Boyle, Maurice Herlihy]

  13. Algorithms

  14. Input Algorithm Output

  15. Input simple and robust model comparable results complexity theory … Algorithm Output

  16. vs. Input Algorithm Output

  17. vs.

  18. The Future of Computing?

  19. Talk Overview Introduction & Motivation SomeExamplesforPhysical Algorithms WhatarePhysical Algorithms?

  20. Well-Known Examples

  21. Small World Phenomenon

  22. Statistical Physics Properties ofrandomgraphs “Static” view

  23. Statistical Physics Properties ofrandomgraphs “Static” view PhysicalAlgorithms People will make decisions [Kleinberg 2000]

  24. Natural Algorithms [Bernard Chazelle, 2009]

  25. ClockSynchronization

  26. Clock Synchronization in Networks Global PositioningSystem (GPS) Radio Clock Signal AC-power lineradiation Synchronizationmessages

  27. Clock Synchronization in Networks Global PositioningSystem (GPS) Radio Clock Signal AC-power lineradiation Synchronizationmessages

  28. Problem: Physical Reality clock rate 1+² 1 1-² t messagedelay ) ) ) ) )

  29. Clock Synchronization in Theory? • Given a communication network • Each node equipped with hardware clock with drift • Message delays with jitter • Goal: Synchronize Clocks (“Logical Clocks”) • Both global and local synchronization! worst-case (but constant)

  30. Time Must Behave! • Time (logical clocks) should not be allowed to stand still or jump

  31. Time Must Behave! • Time (logical clocks) should not be allowed to stand still or jump • Let’s be more careful (and ambitious): • Logical clocks should always move forward • Sometimes faster, sometimes slower is OK. • But there should be a minimum and a maximum speed. • As close to correct time as possible!

  32. Local Skew Tree-based Algorithms NeighborhoodAlgorithms e.g. FTSP e.g. GTSP Bad localskew

  33. … Clockvalue:T-D Clockvalue:T Clockvalue:T-1 Clockvalue:T-D+1 Synchronization Algorithms: An Example (“Amax”) • Question: How to update the logical clock based on the messages from the neighbors? • Idea: Minimizing the skew to the fastestneighbor • Set clock to maximum clock value you know, forward new values immediately • First all messages are slow (1), then suddenly all messages are fast (0)! Fastest Hardware Clock Time is T Time is T Time is T T T skewD

  34. LocalSkew: OverviewofResults Everybody‘s expectation, 10 years ago („solved“) All natural algorithms [Locher et al., DISC 2006] Blocking algorithm Lower bound of logD/ loglogD[Fan & Lynch, PODC 2004] 1logD √D D … Dynamic Networks![Kuhn et al., SPAA 2009] Kappa algorithm[Lenzen et al., FOCS 2008] Dynamic Networks![Kuhn et al., PODC 2010] Tight lower bound[Lenzen et al., PODC 2009] together[JACM 2010]

  35. Experimental Results for Global Skew FTSP PulseSync [Lenzen, Sommer, W, SenSys 2009]

  36. Experimental Results for Global Skew FTSP PulseSync [Lenzen, Sommer, W, SenSys 2009]

  37. Clock Synchronization vs. Car Coordination • In the future cars may travel at high speed despite a tiny safety distance, thanks to advanced sensors and communication

  38. Clock Synchronization vs. Car Coordination • In the future cars may travel at high speed despite a tiny safety distance, thanks to advanced sensors and communication • How fast & close can you drive? • Answer possibly related to clock synchronization • clock drift ↔ cars cannot control speed perfectly • message jitter ↔ sensors or communication between cars not perfect

  39. Wireless Communication

  40. Wireless Communication EE, Physics Maxwell Equations Simulation, Testing ‘Scaling Laws’ Network Algorithms CS, Applied Math [Geometric] Graphs Worst-Case Analysis Any-Case Analysis

  41. CS Models: e.g. Disk Model (Protocol Model) ReceptionRange InterferenceRange

  42. EE Models: e.g. SINR Model (Physical Model)

  43. Signal-To-Interference-Plus-Noise Ratio (SINR) Formula Received signal power from sender Power level of sender u Path-loss exponent Minimum signal-to-interference ratio Noise Distance between two nodes Received signal power from all other nodes (=interference)

  44. Example: Protocol vs. Physical Model Assume a single frequency (and no fancy decoding techniques!) Let =3, =3, and N=10nW Transmission powers: PB= -15 dBm and PA= 1 dBm SINR of A at D: SINR of B at C: C D B A 4m 1m 2m NO Protocol Model Is spatial reuse possible? YES With power control

  45. This works in practice! … even with very simple hardware (sensor nodes) u1 u2 u3 u4 u5 u6 Time for transmitting 20‘000 packets: Speed-up is almost a factor 3 [Moscibroda, W, Weber, Hotnets 2006]

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