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The Topological Structure of Asynchronous Computability
 JOURNAL OF THE ACM
, 1996
"... We give necessary and sufficient combinatorial conditions characterizing the tasks that can be solved by asynchronous processes, of which all but one can fail, that communicate by reading and writing a shared memory. We introduce a new formalism for tasks, based on notions from classical algebra ..."
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Cited by 117 (11 self)
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We give necessary and sufficient combinatorial conditions characterizing the tasks that can be solved by asynchronous processes, of which all but one can fail, that communicate by reading and writing a shared memory. We introduce a new formalism for tasks, based on notions from classical algebraic and combinatorial topology, in which a task's possible input and output values are each associated with highdimensional geometric structures called simplicial complexes. We characterize computability in terms of the topological properties of these complexes. This characterization has a surprising geometric interpretation: a task is solvable if and only if the complex representing the task's allowable inputs can be mapped to the complex representing the task's allowable outputs by a function satisfying certain simple regularity properties. Our formalism thus replaces the "operational" notion of a waitfree decision task, expressed in terms of interleaved computations unfolding ...
WaitFree Algorithms for Fast, LongLived Renaming
 Science of Computer Programming
, 1995
"... We consider waitfree solutions to the renaming problem for sharedmemory multiprocessing systems [3, 5]. In the renaming problem, processes are required to choose new names in order to reduce the size of their name space. Previous solutions to the renaming problem have time complexity that is depen ..."
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Cited by 74 (15 self)
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We consider waitfree solutions to the renaming problem for sharedmemory multiprocessing systems [3, 5]. In the renaming problem, processes are required to choose new names in order to reduce the size of their name space. Previous solutions to the renaming problem have time complexity that is dependent on the size of the original name space, and allow processes to acquire names only once. In this paper, we present several new renaming algorithms. Most of our algorithms have time complexity that is independent of the size of the original name space, and some of our algorithms solve a new, more general version of the renaming problem called longlived renaming. In longlived renaming algorithms, processes may repeatedly acquire and release names. 1 Introduction In the M renaming problem [2], each of k processes is required to choose a distinct value, called a name, that ranges over f0; :::; M \Gamma 1g. Each process is assumed to have a unique process identifier ranging over f0::N \...
Hundreds of Impossibility Results for Distributed Computing
 Distributed Computing
, 2003
"... We survey results from distributed computing that show tasks to be impossible, either outright or within given resource bounds, in various models. The parameters of the models considered include synchrony, faulttolerance, different communication media, and randomization. The resource bounds refe ..."
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Cited by 40 (4 self)
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We survey results from distributed computing that show tasks to be impossible, either outright or within given resource bounds, in various models. The parameters of the models considered include synchrony, faulttolerance, different communication media, and randomization. The resource bounds refer to time, space and message complexity. These results are useful in understanding the inherent difficulty of individual problems and in studying the power of different models of distributed computing.
A simple constructive computability theorem for waitfree computation
 In: Proceedings of the 1994 ACM Symposium on Theory of Computing 243–252
, 1994
"... I ..."
A Simple Algorithmically Reasoned Characterization of Waitfree Computations
 In Proceedings of the 16th Annual ACM Symposium on Principles of Distributed Computing
, 1996
"... ) Elizabeth Borowsky (borowsky@hpl.hp.com) HewlettPackard Laboratories PaloAlto, CA 94303 U.S.A. Eli Gafni (eli@cs.ucla.edu) Computer Science Department University of California, Los Angeles Los Angeles, CA 90024 U.S.A. July 1, 1996 Abstract In a sequence of two pioneering papers Herlihy and S ..."
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Cited by 34 (11 self)
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) Elizabeth Borowsky (borowsky@hpl.hp.com) HewlettPackard Laboratories PaloAlto, CA 94303 U.S.A. Eli Gafni (eli@cs.ucla.edu) Computer Science Department University of California, Los Angeles Los Angeles, CA 90024 U.S.A. July 1, 1996 Abstract In a sequence of two pioneering papers Herlihy and Shavit characterized waitfree sharedmemory computations. The derivation of the characterization involves homology for the necessary conditions, and complex geometry arguments for the sufficiency. This paper gives an alternative proof of the conditions using familiar algorithmic arguments. Our only reliance on geometry is the use of a corollary to the simplicial approximation. Furthermore, this paper is the first to present another consequence of the relation between distributed algorithms and topology: that certain theorems in topology are naturally proven by distributed algorithms interpretations. Our techniques can be extended to characterize models that are more complex than the waitfree...
An Adaptive Collect Algorithm with Applications
 Distributed Computing
, 2001
"... In a sharedmemory distributed system, n independent asynchronous processes communicate by reading and writing to shared memory. An algorithm is adaptive (to total contention) if its step complexity depends only on the actual number, k, of active processes in the execution; this number is unknown ..."
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Cited by 32 (10 self)
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In a sharedmemory distributed system, n independent asynchronous processes communicate by reading and writing to shared memory. An algorithm is adaptive (to total contention) if its step complexity depends only on the actual number, k, of active processes in the execution; this number is unknown in advance and may change in different executions of the algorithm. Adaptive algorithms are inherently waitfree, providing faulttolerance in the presence of an arbitrary number of crash failures and different processes' speed. A waitfree adaptive collect algorithm with O(k) step complexity is presented, together with its applications in waitfree adaptive algorithms for atomic snapshots, immediate snapshots and renaming. Keywords: contentionsensitive complexity, waitfree algorithms, asynchronous sharedmemory systems, read/write registers, atomic snapshots, immediate atomic snapshots, renaming. Work supported by the fund for the promotion of research in the Technion. y Department of Computer Science, The Technion, Haifa 32000, Israel. hagit@cs.technion.ac.il. z Department of Computer Science, The Technion, Haifa 32000, Israel. leonf@cs.technion.ac.il. x Computer Science Department, UCLA. eli@cs.ucla.edu. 1
LongLived Renaming Made Fast
, 1995
"... In the longlived renaming problem  a generalization of the classical onetime renaming problem  n processors with unique names ranging over a source name space f0; : : : ; S \Gamma 1g repeatedly acquire and release unique names from a (smaller) destination name space f0; : : : ; D \Gamma 1g. ..."
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Cited by 24 (7 self)
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In the longlived renaming problem  a generalization of the classical onetime renaming problem  n processors with unique names ranging over a source name space f0; : : : ; S \Gamma 1g repeatedly acquire and release unique names from a (smaller) destination name space f0; : : : ; D \Gamma 1g. It is assumed that at most k out of n processors concurrently request or hold names. An efficient renaming protocol provides a useful frontend for protocols whose time complexity depends on the size of the name space containing the participating processes. We consider longlived renaming in the context of asynchronous, sharedmemory multiprocessing systems that provide only read and write operations. A renaming protocol is fast iff the time complexity of acquiring and releasing a name is polynomial in k and independent of n and S. We present a waitfree, read/write protocol for longlived renaming that achieves a destination name space of size O(k 2 ) with time complexity O(k 3 ). If ...
The Combinatorial Structure of Waitfree Solvable Tasks (Extended Abstract)
, 1996
"... This paper presents a selfcontained study of waitfree solvable tasks. A new necessary and sufficient condition for waitfree solvability is proved, providing a characterization of the waitfree solvable tasks. The necessary condition is used to prove tight bounds on renaming and kset consensus. ..."
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Cited by 24 (13 self)
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This paper presents a selfcontained study of waitfree solvable tasks. A new necessary and sufficient condition for waitfree solvability is proved, providing a characterization of the waitfree solvable tasks. The necessary condition is used to prove tight bounds on renaming and kset consensus. The framework is based on topology, but uses only elementary combinatorics, and does not rely on algebraic or geometric arguments.
Adaptive and Efficient Algorithms for Lattice Agreement and Renaming
 SIAM J. Comput
, 1998
"... In a sharedmemory system, n independent asynchronous processes, with distinct names in the range {0, ..., N  1}, communicate by reading and writing to shared registers. An algorithm is waitfree if a process completes its execution regardless of the behavior of other processes. This paper consider ..."
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Cited by 23 (7 self)
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In a sharedmemory system, n independent asynchronous processes, with distinct names in the range {0, ..., N  1}, communicate by reading and writing to shared registers. An algorithm is waitfree if a process completes its execution regardless of the behavior of other processes. This paper considers waitfree algorithms whose complexity adjusts to the level of contention in the system: An algorithm is adaptive (to total contention) if its step complexity depends only on the actual number of active processes, k; this number is unknown in advance and may change in different executions of the algorithm. Adaptive algorithms are presented for two important decision problems, lattice agreement and (6k  1)renaming; the step complexity of both algorithms is O(k log k). An interesting component of the (6k  1)renaming algorithm is an O(N) algorithm for (2k  1)renaming; this improves on the best previously known (2k  1)renaming algorithm, which has O(Nnk) s...
Using kExclusion to Implement Resilient, Scalable Shared Objects (Extended Abstract)
 in Proceedings of the 13th Annual ACM Symposium on Principles of Distributed Computing
, 1994
"... ) James H. Anderson and Mark Moir Department of Computer Science The University of North Carolina at Chapel Hill Chapel Hill, North Carolina 275993175, USA Abstract We present a methodology for the implementation of resilient shared objects that allows the desired level of resiliency to be selecte ..."
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Cited by 19 (6 self)
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) James H. Anderson and Mark Moir Department of Computer Science The University of North Carolina at Chapel Hill Chapel Hill, North Carolina 275993175, USA Abstract We present a methodology for the implementation of resilient shared objects that allows the desired level of resiliency to be selected based on performance concerns. This methodology is based on the kexclusion and renaming problems. To make this methodology practical, we present a number of fast kexclusion algorithms that employ "local spin" techniques to minimize the impact of the processortomemory bottleneck. We also present a new "longlived" renaming algorithm. Our k exclusion algorithms are based on commonlyavailable synchronization primitives, are fast in the absence of contention, and have scalable performance when contention exceeds expected thresholds. By contrast, all prior kexclusion algorithms either require unrealistic atomic operations or perform badly. Our kexclusion algorithms are also the first ...