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24
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 47 (5 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.
Randomized dining philosophers to tdma scheduling in wireless sensor networks
, 2004
"... Abstract — A randomized dining philosophers algorithm is presented for a realistic semisynchronous model where message delays vary within an unknown bound, and clocks may run at a different speed without any synchronization. In order to predict the unknown bounds, the algorithm employs a simple net ..."
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Cited by 25 (1 self)
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Abstract — A randomized dining philosophers algorithm is presented for a realistic semisynchronous model where message delays vary within an unknown bound, and clocks may run at a different speed without any synchronization. In order to predict the unknown bounds, the algorithm employs a simple network delay measurement technique. The algorithm has an expected running time and message complexity of ¢¡¤£¦ ¥ with high probability. £ is the maximum number of contenders for a process in the system (while £¨§�©, © being the total number of processes). A version of the algorithm, called DRAND, is shown to be used for TDMA scheduling or channel assignment for wireless networks. This algorithm is the first scalable implementation of RAND, a commonly used, centralized channel assignment algorithm. The algorithm can also be used for distributed graph coloring in a semisynchronous environment. Given any general graph, the algorithm produces a chromatic number up to £���� (in this case, £ is the maximum number of edges). Compared to existing algorithms on distributed graph coloring in the PRAM model, the algorithm can generate equal or less number of colors; often, far less than £��� �. DRAND is implemented in TinyOS and tested in a real wireless sensor network with Mica2 nodes. The experiment shows that DRAND is scalable and robust in a real wireless network setting. I.
Finitary Fairness
"... Fairness is a mathematical abstraction: in a multiprogramming environment, fairness abstracts the details of admissible ("fair") schedulers; in a distributed environment, fairness abstracts the relative speeds of processors. We argue that the standard definition of fairness often is unnece ..."
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Cited by 25 (4 self)
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Fairness is a mathematical abstraction: in a multiprogramming environment, fairness abstracts the details of admissible ("fair") schedulers; in a distributed environment, fairness abstracts the relative speeds of processors. We argue that the standard definition of fairness often is unnecessarily weak and can be replaced by the stronger, yet still abstract, notion of finitary fairness. While standard weak fairness requires that no enabled transition is postponed forever, finitary weak fairness requires that for every computation of a system there is an unknown bound k such that no enabled transition is postponed more than k consecutive times. In general, the finitary restriction n(F) of any given fairness requirement F is the union of all !regular safety properties contained in F. The adequacy of the proposed abstraction is shown in two ways. Suppose we prove a program property under the assumption of finitary fairness. In a multiprogramming environment, the program then satisfies the property for all fair finitestate schedulers. In a distributed environment, the program then satisfies the property for all choices of lower and upper bounds on the speeds (or timings) of processors. The bene ts of nitary fairness are twofold. First, the proof rules for verifying liveness properties of concurrent programs are simplified: wellfounded induction over the natural numbers is adequate to prove termination under finitary fairness. Second, the fundamental problem of consensus in a faulty asynchronous distributed environment can be solved assuming finitary fairness.
RealTime Object Sharing with Minimal System Support (Extended Abstract)
 In Proceedings of the 15th Annual ACM Symposium on Principles of Distributed Computing
, 1996
"... ) Srikanth Ramamurthy, Mark Moir, and James H. Anderson Department of Computer Science, University of North Carolina at Chapel Hill Abstract We show that, for a large class of hard realtime systems, any object with consensus number P in Herlihy's waitfree hierarchy is universal for any numbe ..."
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Cited by 22 (6 self)
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) Srikanth Ramamurthy, Mark Moir, and James H. Anderson Department of Computer Science, University of North Carolina at Chapel Hill Abstract We show that, for a large class of hard realtime systems, any object with consensus number P in Herlihy's waitfree hierarchy is universal for any number of tasks executing on P processors. These results exploit characteristics of prioritybased schedulers common to most hard realtime systems. An important special case of this result is that, for hard realtime applications on uniprocessors, reads and writes are universal. Thus, Herlihy's hierarchy collapses for such applications. 1 Introduction This paper is concerned with implementations of shared objects in hard realtime systems. A hard realtime system is comprised of a collection of tasks that execute on one or more processors. A task is a sequential program that may be invoked repeatedly in response to an external stimulus or timer. Each invocation of a task must complete execution by ...
Stabilizing TimeAdaptive Protocols
, 1998
"... We study the scenario where a transient batch of faults hit a minority of the nodes in a distributed system by corrupting their state. We concentrate on the basic persistent bit problem, where the system is required to maintain a 0/1 value in the face of transient failures by means of replication ..."
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Cited by 21 (4 self)
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We study the scenario where a transient batch of faults hit a minority of the nodes in a distributed system by corrupting their state. We concentrate on the basic persistent bit problem, where the system is required to maintain a 0/1 value in the face of transient failures by means of replication. We give an algorithm to stabilize the value to a correct state quickly; that is, denoting the unknown number of faulty nodes by f , our algorithm recovers the value of the bit at all nodes in O(f) time units for any f ! n=2, where n is the number of all nodes. Moreover,
ObstructionFree algorithms can be practically waitfree
 In Distributed Algorithms, P. Fraigniaud, Ed. Lecture Notes in Computer Science
, 2005
"... Abstract. The obstructionfree progress condition is weaker than previous nonblocking progress conditions such as lockfreedom and waitfreedom, and admits simpler implementations that are faster in the uncontended case. Pragmatic contention management techniques appear to be effective at facilitatin ..."
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Abstract. The obstructionfree progress condition is weaker than previous nonblocking progress conditions such as lockfreedom and waitfreedom, and admits simpler implementations that are faster in the uncontended case. Pragmatic contention management techniques appear to be effective at facilitating progress in practice, but, as far as we know, none guarantees progress. We present a transformation that converts any obstructionfree algorithm into one that is waitfree when analyzed in the unknownbound semisynchronous model. Because all practical systems satisfy the assumptions of the unknownbound model, our result implies that, for all practical purposes, obstructionfree implementations can provide progress guarantees equivalent to waitfreedom. Our transformation preserves the advantages of any pragmatic contention manager, while guaranteeing progress. 1
Fast Timingbased Algorithms
 Distributed Computing
, 1996
"... Concurrent systems in which there is a known upper bound \Delta on memory access time are considered. Two prototypical synchronization problems, mutual exclusion and consensus, are studied and solutions that have constant (i.e. independent of \Delta and the total number of processes) time complexity ..."
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Cited by 15 (4 self)
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Concurrent systems in which there is a known upper bound \Delta on memory access time are considered. Two prototypical synchronization problems, mutual exclusion and consensus, are studied and solutions that have constant (i.e. independent of \Delta and the total number of processes) time complexity in the absence of contention are presented. For mutual exclusion, in the absence of contention, a process needs only five accesses to the shared memory to enter its critical section, and in the presence of contention, the winning process may need to delay itself for 4 \Delta \Delta time units. For consensus, in absence of contention, a process decides after four accesses to the shared memory, and in the presence of contention, it may need to delay itself for \Delta time units. 1 Introduction The possibility and complexity of synchronization in a distributed environment depends heavily on timing assumptions. In the asynchronous model no timing assumptions are made about the relative speeds ...
Verification Methods for the Divergent Runs Of Clock Systems
 FTRTFT 94: Formal Techniques in Realtime and Faulttolerant Systems, Lecture Notes in Computer Science 863
, 1994
"... We present a methodology for proving temporal properties of the divergent runs of reactive systems with realvalued clocks. A run diverges if time advances beyond any bound. Since the divergent runs of a system may satisfy liveness properties that are not satisfied by some convergent runs, the st ..."
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Cited by 8 (1 self)
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We present a methodology for proving temporal properties of the divergent runs of reactive systems with realvalued clocks. A run diverges if time advances beyond any bound. Since the divergent runs of a system may satisfy liveness properties that are not satisfied by some convergent runs, the standard proof rules are incomplete if only divergent runs are considered.
Efficient Transformations of ObstructionFree Algorithms into Nonblocking Algorithms
"... Abstract. Three well studied progress conditions for implementing concurrent algorithms without locking are, obstructionfreedom, nonblocking and waitfreedom. Obstructionfreedom is weaker than nonblocking which, in turn, is weaker than waitfreedom. While obstructionfreedom and nonblocking hav ..."
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Cited by 5 (1 self)
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Abstract. Three well studied progress conditions for implementing concurrent algorithms without locking are, obstructionfreedom, nonblocking and waitfreedom. Obstructionfreedom is weaker than nonblocking which, in turn, is weaker than waitfreedom. While obstructionfreedom and nonblocking have the potential to significantly improve the performance of concurrent applications, waitfreedom (although desirable) imposes too much overhead upon the implementation. In [5], Fich, Luchangco, Moir, and Shavit have presented an interesting transformation that converts any obstructionfree algorithm into a waitfree algorithm when analyzed in the unknownbound semisynchronous model. The FLMS transformation uses n atomic singlewriter registers, n atomic multiwriter registers and a single fetchandincrement object, where n is the number of processes. We define a time complexity measure for analyzing such transformations, and prove that the time complexity of the FLMS transformation is exponential in the number of processes n. This leads naturally to the question of whether the time and/or space complexity of the FLMS transformation can be improved by relaxing the waitfreedom progress condition. We present several efficient transformations that convert any obstructionfree algorithm into a nonblocking algorithm when analyzed in the unknownbound semisynchronous model. All our transformations have O(1) time complexity. One transformation uses n atomic singlewriter registers and a single compareandswap object; another transformation uses only a single compareandswap object which is assumed to support also a read operation.