(anti-Ω x × Σ z )-based k-set agreement algorithms

This paper considers the k-set agreement problem in a crashprone asynchronous message passing system enriched with failure detectors. Two classes of failure detectors have been previously identified as necessary to solve asynchronous k-set agreement: the class anti-leader anti-Ωk and the weak-quorum class Σk. The paper investigates the families of failure detector (anti-Ωx)1≤x≤n and (Σz)1≤z≤n. It characterizes in an n processes system equipped with failure detectors anti-Ωx and Σz for which values of k, x and z k-set-agreement can be solved. While doing so, the paper (1) disproves previous conjunctures about the weakest failure detector to solve k-set-agreement in the asynchronous message passing model and, (2) introduces the first indulgent algorithm that tolerates a majority of processes failures.

[1]  Rachid Guerraoui,et al.  The inherent price of indulgence , 2002, PODC '02.

[2]  Eli Gafni,et al.  Structured derivations of consensus algorithms for failure detectors , 1998, PODC '98.

[3]  Gil Neiger.  Failure detectors and the wait-free hierarchy (extended abstract) , 1995, PODC '95.

[4]  M. Raynal,et al.  Looking for the Weakest Failure Detector for k-Set Agreement in Message-Passing Systems: Is Πk the End of the Road? , 1929 .

[5]  Gil Neiger,et al.  Failure Detectors and the Wait-Free Hierarchy. , 1995, ACM SIGACT-SIGOPS Symposium on Principles of Distributed Computing.

[6]  Achour Mostéfaoui,et al.  On the computability power and the robustness of set agreement-oriented failure detector classes , 2008, Distributed Computing.

[7]  Nancy A. Lynch,et al.  On the weakest failure detector ever , 2007, PODC.

[8]  Achour Mostéfaoui,et al.  k-set agreement with limited accuracy failure detectors , 2000, PODC '00.

[9]  Antonio Fernandez Anta,et al.  Weakest failure detectors via an egg-laying simulation ( Preliminary Version ) , 2009 .

[10]  Nancy A. Lynch,et al.  Impossibility of distributed consensus with one faulty process , 1985, JACM.

[11]  Rachid Guerraoui,et al.  The Weakest Failure Detector for Message Passing Set-Agreement , 2008, DISC.

[12]  Sam Toueg,et al.  Unreliable failure detectors for reliable distributed systems , 1996, JACM.

[13]  Rachid Guerraoui,et al.  The Alpha of Indulgent Consensus , 2007, Comput. J..

[14]  Wei Chen,et al.  Weakening Failure Detectors for k -Set Agreement Via the Partition Approach , 2007, DISC.

[15]  Sam Toueg,et al.  The weakest failure detector for solving consensus , 1992, PODC '92.

[16]  Soma Chaudhuri,et al.  More Choices Allow More Faults: Set Consensus Problems in Totally Asynchronous Systems , 1993, Inf. Comput..

[17]  Petr Kuznetsov,et al.  The weakest failure detector for solving k-set agreement , 2009, PODC '09.

[18]  Maurice Herlihy,et al.  Tight Bounds for K-set Agreement with Limited-scope Failure Detectors , 2003, PODC.

[19]  Michel Raynal,et al.  Looking for the Weakest Failure Detector for k-Set Agreement in Message-Passing Systems: Is ${\it \Pi}_k${\it \Pi}_k the End of the Road? , 2009, SSS.

[20]  Piotr Zielinski.  Anti-Ω: the weakest failure detector for set agreement , 2008, PODC '08.

[21]  Antonio Fernández,et al.  Brief announcement: weakest failure detectors via an egg-laying simulation , 2009, PODC '09.

[22]  Rachid Guerraoui,et al.  Sharing is harder than agreeing , 2008, PODC '08.

[23]  Michel Raynal,et al.  A simple proof of the necessity of the failure detector Sigma to implement an atomic register in asynchronous message-passing systems , 2010, Inf. Process. Lett..

[24]  Rachid Guerraoui,et al.  The weakest failure detectors to solve certain fundamental problems in distributed computing , 2004, PODC '04.

[25]  Michael E. Saks,et al.  Wait-free k-set agreement is impossible: the topology of public knowledge , 1993, STOC.

[26]  Eli Gafni,et al.  Generalized FLP impossibility result for t-resilient asynchronous computations , 1993, STOC.

[27]  Maurice Herlihy,et al.  The topological structure of asynchronous computability , 1999, JACM.

[28]  Dan Alistarh,et al.  Of Choices, Failures and Asynchrony: The Many Faces of Set Agreement , 2011, Algorithmica.

[29]  Michel Raynal,et al.  In Search of the Holy Grail: Looking for the Weakest Failure Detector for Wait-Free Set Agreement , 2006, OPODIS.

[30]  Nancy A. Lynch,et al.  A general characterization of indulgence , 2008, TAAS.

[31]  Rachid Guerraoui,et al.  Indulgent algorithms (preliminary version) , 2000, PODC '00.