Anti-Ω: the weakest failure detector for set agreement

In the set agreement problem, n processes have to decide on at most n − 1 of the proposed values. This paper considers asynchronous shared-memory systems equipped with an anti-Ω failure detector. Each query to the anti-Ω returns a process id; the specification ensures that there is a correct process whose id is returned only finitely many times. The main result is that anti-Ω is both necessary and sufficient to solve set agreement in the asynchronous shared memory model.

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

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

[3]  Michel Raynal,et al.  Simultaneous Consensus Tasks: A Tighter Characterization of Set-Consensus , 2006, ICDCN.

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

[5]  Eli Gafni,et al.  Immediate atomic snapshots and fast renaming , 1993, PODC '93.

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

[7]  Maurice Herlihy,et al.  Subconsensus Tasks: Renaming Is Weaker Than Set Agreement , 2006, DISC.

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

[9]  Wei Chen,et al.  On Failure Detectors Weaker Than Ever , 2007 .

[10]  Michel Raynal,et al.  The k-simultaneous consensus problem , 2010, Distributed Computing.

[11]  Achour Mostéfaoui,et al.  Exploring Gafni's Reduction Land: From Omegak to Wait-Free Adaptive (2p-[p/k])-Renaming Via k-Set Agreement , 2006, DISC.

[12]  Michel Raynal,et al.  Test & Set, Adaptive Renaming and Set Agreement: a Guided Visit to Asynchronous Computability , 2007, 2007 26th IEEE International Symposium on Reliable Distributed Systems (SRDS 2007).

[13]  Leslie Lamport,et al.  Disk Paxos , 2003, Distributed Computing.

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

[15]  Rachid Guerraoui,et al.  Shared Memory vs Message Passing , 2003 .

[16]  Hagit Attiya.  A direct lower bound for k-set consensus , 1998, PODC '98.

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

[18]  Eli Gafni,et al.  Immediate Atomic Snapshots and Fast Renaming (Extended Abstract). , 1993, PODC 1993.

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

[20]  Sam Toueg,et al.  Every problem has a weakest failure detector , 2008, PODC '08.

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

[22]  Achour Mostéfaoui,et al.  Irreducibility and additivity of set agreement-oriented failure detector classes , 2006, PODC '06.

[23]  Eli Gafni,et al.  Three-Processor Tasks Are Undecidable , 1999, SIAM J. Comput..

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

[25]  Piotr Zielinski.  Automatic Classification of Eventual Failure Detectors , 2007, DISC.

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

[27]  Rachid Guerraoui,et al.  On the Weakest Failure Detector for Non-Blocking Atomic Commit , 2002, IFIP TCS.

[28]  Yehuda Afek,et al.  Long-lived and adaptive atomic snapshot and immediate snapshot (extended abstract) , 2000, PODC '00.

[29]  Vassos Hadzilacos,et al.  Using Failure Detectors to Solve Consensus in Asynchronous Sharde-Memory Systems (Extended Abstract) , 1994, WDAG.

[30]  Rachid Guerraoui,et al.  Finally the Weakest Failure Detector for Non-Blocking Atomic Commit , 2003 .

[31]  Eli Gafni.  Read-Write Reductions , 2006, ICDCN.

[32]  Michel Raynal,et al.  Failure Detectors as Schedulers (An Algorithmically-Reasoned Characterization) , 2007 .

[33]  Yehuda Afek,et al.  Failure detectors in loosely named systems , 2008, PODC '08.

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

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