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An Evaluation of Communication-Optimal  P Algorithms

An Evaluation of Communication-Optimal  P Algorithms. Mikel Larrea Iratxe Soraluze Roberto Cortiñas Alberto Lafuente Department of Computer Architecture and Technology The University of the Basque Country. Contents. Motivation System Model Communication Optimality The Algorithms

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An Evaluation of Communication-Optimal  P Algorithms

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  1. An Evaluationof Communication-OptimalP Algorithms Mikel Larrea Iratxe Soraluze Roberto Cortiñas Alberto Lafuente Department of Computer Architecture and Technology The University of the Basque Country

  2. Contents • Motivation • System Model • Communication Optimality • The Algorithms • Complexity Analysis • Performance Evaluation • Conclusion PDP 2008 − Toulouse, France, February 13-15, 2008

  3. Motivation • Unreliable failure detectors have been used to address Consensus and related problems in asynchronous crash-prone distributed systems • Theory: impossibility/possibility results, minimality results • Practice: efficient implementations and transformations • The P class satisfies the following properties • Strong Completeness: eventually every process that crashes is permanently suspected by every correct process • Eventual Strong Accuracy: there is a time after which correct processes are not suspected by any correct process PDP 2008 − Toulouse, France, February 13-15, 2008

  4. } ring-based Motivation:Implementing P Efficiently • Communication efficiency • Number of links used forever • Periodic communication cost • Non communication-efficient algorithms • Communication-efficient algorithms • Communication-optimal algorithms • Sporadic communication overhead • Number of messages to manage a suspicion • Quality of Service • Query accuracy probability • Crash detection latency PDP 2008 − Toulouse, France, February 13-15, 2008

  5. System Model • Finite set of n processes  = {p1, p2, ..., pn} that communicate only by message-passing • Every pair of processes is connected by two unidirectional and reliable communication links, one in each direction • Processes can fail by crashing. Once a process crashes, it does not recover • Up to n-1 processes may crash • C is the (unknown) number of correct processes • Processes are arranged in a logical ring • Partially synchronous system PDP 2008 − Toulouse, France, February 13-15, 2008

  6. p1 p2 p6 p5 p3 p4 Communication Optimality A ring arrangement of processes PDP 2008 − Toulouse, France, February 13-15, 2008

  7. p1 p2 p6 p5 p3 p4 Communication Optimality Communication-efficient algorithms: n links are used forever PDP 2008 − Toulouse, France, February 13-15, 2008

  8. p1 p2 p6 p5 p3 p4 Communication Optimality Communication-optimal algorithms: C links are used forever PDP 2008 − Toulouse, France, February 13-15, 2008

  9. The Algorithms • We have implemented several ring-based communication-optimalPalgorithms • Algorithms are based on reporting failure suspicions (and suspicion refutations) • Three communication patterns • Algorithm 1: based on Reliable Broadcast • RBcast is a communication primitive guaranteeing that all correct processes deliver the same set of messages. This set includes at least all messages broadcast by correct processes • Algorithm 2: based on one-to-one communication • Algorithm 3: based on one-to-all communication PDP 2008 − Toulouse, France, February 13-15, 2008

  10. p1 p2 p6 p5 p3 p4 The Algorithms Algorithm 1: RBcast-based • O(n2) messages required to communicate a suspicion • Low crash detection latency PDP 2008 − Toulouse, France, February 13-15, 2008

  11. p1 Suspected1= {p3, p5, p6} p2 p6 p5 p3 p4 The Algorithms Algorithm 2: one-to-one based • O(n) messages required to communicate a suspicion • High crash detection latency PDP 2008 − Toulouse, France, February 13-15, 2008

  12. p1 Suspected1= {p3, p5, p6} p2 p6 p5 p3 p4 The Algorithms Algorithm 3: one-to-all based • O(n) messages required to communicate a suspicion • Low crash detection latency PDP 2008 − Toulouse, France, February 13-15, 2008

  13. Complexity Analysis PDP 2008 − Toulouse, France, February 13-15, 2008

  14. Performance Evaluation:Query Accuracy PDP 2008 − Toulouse, France, February 13-15, 2008

  15. Performance Evaluation:Crash Detection Latency PDP 2008 − Toulouse, France, February 13-15, 2008

  16. Conclusion • We have presented several communication-optimal algorithms implementing P • Which to use: Algorithm 2 or Algorithm 3? • Best choice: hybrid approach • Initially (erroneous suspicions), use Algorithm 2 • When the ring has probably stabilized, switch to Algorithm 3 • Issues • What about crashes during stabilization? • How do we know (guess) that the system has stabilized? PDP 2008 − Toulouse, France, February 13-15, 2008

  17. Questions ? PDP 2008 − Toulouse, France, February 13-15, 2008

  18. Future Work • Current scenario: • Local area network settings • Uniform communication delays • 1-to-all communication supported easily (Ethernet, WiFi) • Future scenario: • Wide area network settings • Non-uniform communication delays • 1-to-all communication not supported • Local communication patterns required • For periodic messages (heartbeats)  ring • For sporadic messages (suspicions and refutations) PDP 2008 − Toulouse, France, February 13-15, 2008

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