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Optimal Scheduling for Disconnected Cooperation
, 2001
"... We consider a distributed environment consisting of n processors that need to perform t tasks. We assume that communication is initially unavailable and that processors begin work in isolation. At some unknown point of time an unknown collection of processors may establish communication. Before proc ..."
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We consider a distributed environment consisting of n processors that need to perform t tasks. We assume that communication is initially unavailable and that processors begin work in isolation. At some unknown point of time an unknown collection of processors may establish communication. Before processors begin communication they execute tasks in the order given by their schedules. Our goal is to schedule work of isolated processors so that when communication is established for the rst time, the number of redundantly executed tasks is controlled. We quantify worst case redundancy as a function of processor advancements through their schedules. In this work we rene and simplify an extant deterministic construction for schedules with n t, and we develop a new analysis of its waste. The new analysis shows that for any pair of schedules, the number of redundant tasks can be controlled for the entire range of t tasks. Our new result is asymptotically optimal: the tails of these schedules are within a 1 +O(n 1 4 ) factor of the lower bound. We also present two new deterministic constructions one for t n, and the other for t n 3=2 , which substantially improve pairwise waste for all prexes of length t= p n, and oer near optimal waste for the tails of the schedules. Finally, we present bounds for waste of any collection of k 2 processors for both deterministic and randomized constructions. 1
Collective asynchronous reading with polylogarithmic worstcase overhead
 in Proceedings, 36th ACM Symposium on Theory of Computing (STOC), 2004
"... The Collect problem for an asynchronous sharedmemory system has the objective for the processors to learn all values of a collection of shared registers, while minimizing the total number of read and write operations. First abstracted by Saks, Shavit, and Woll [37], Collect is among the standard pr ..."
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The Collect problem for an asynchronous sharedmemory system has the objective for the processors to learn all values of a collection of shared registers, while minimizing the total number of read and write operations. First abstracted by Saks, Shavit, and Woll [37], Collect is among the standard problems in distributed computing, The model consists of n asynchronous processes, each with a singlewriter multireader register of a polynomial capacity. The best previously known deterministic solution performs O(n 3/2 log n) reads and writes, and it is due to Ajtai, Aspnes, Dwork, and Waarts [3]. This paper presents a new deterministic algorithm that performs O(n log 7 n) read/write operations, thus substantially improving the best previous upper bound. Using an approach based on epidemic rumorspreading, the novelty of the new algorithm is in using a family of expander graphs and ensuring
Atmostonce semantics in asynchronous shared memory
 In DISC
, 2009
"... Abstract. Atmostonce semantics is one of the standard models for object access in decentralized systems. Accessing an object, such as altering the state of the object by means of direct access, method invocation, or remote procedure call, with atmostonce semantics guarantees that the access is ..."
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Abstract. Atmostonce semantics is one of the standard models for object access in decentralized systems. Accessing an object, such as altering the state of the object by means of direct access, method invocation, or remote procedure call, with atmostonce semantics guarantees that the access is not repeated morethanonce, enabling one to reason about the safety properties of the object. This paper investigates implementations of atmostonce access semantics in a model where a set of such actions is to be performed by a set of failureprone, asynchronous sharedmemory processes. We introduce a definition of the atmostonce problem for performing a set of n jobs using m processors and we introduce a notion of efficiency for such protocols, called effectiveness, used to classify algorithms. Effectiveness measures the number of jobs safely completed by an implementation, as a function of the overall number of jobs n, the number of participating processes m, and the number of process crashes f in the presence of an adversary. We prove a lower bound of n−f on the effectiveness of any algorithm. We then prove that this lower bound can be matched in the two process setting by presenting two algorithms that offer a tradeoff between time and space complexity. Finally, we generalize our twoprocess solution in the multiprocess setting with a hierarchical algorithm that achieves effectiveness of n−logm·o(n), coming reasonably close, asymptotically, to the corresponding lower bound. 1
A Method for Creating NearOptimal Instances of a Certified WriteAll Algorithm
 11th Annual European Symposium on Algorithms (ESA’03
, 2003
"... This paper shows how to create nearoptimal instances of the Certified WriteAll algorithm called AWT that was introduced by Anderson and Woll [2]. This algorithm is the best known deterministic algorithm that can be used to simulate n synchronous parallel processors on n asynchronous processors. In ..."
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This paper shows how to create nearoptimal instances of the Certified WriteAll algorithm called AWT that was introduced by Anderson and Woll [2]. This algorithm is the best known deterministic algorithm that can be used to simulate n synchronous parallel processors on n asynchronous processors. In this algorithm n processors update n memory cells and then signal the completion of the updates. The algorithm is instantiated with q permutations, where q can be chosen from a wide range of values. When implementing a simulation on a specific parallel system with n processors, one would like to use an instance of the algorithm with the best possible value of q, in order to maximize the efficiency of the simulation. This paper shows that the choice of q is critical for obtaining an instance of the AWT algorithm with nearoptimal work. For any > 0, and any large enough n, work of any instance of the algorithm must be at least n . Under certain conditions, however, that q is about e and for infinitely many large enough n, this lower bound can be nearly attained by instances of the algorithm with work at most n . The paper also shows a penalty for not selecting q well. When q is significantly away from e , then work of any instance of the algorithm with this displaced q must be considerably higher than otherwise.
How to Allocate Tasks Asynchronously
"... Abstract—Asynchronous task allocation is a fundamental problem in distributed computing in which p asynchronous processes must execute a set of m tasks. Also known as writeall or doall, this problem been studied extensively, both independently and as a key building block for various distributed al ..."
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Abstract—Asynchronous task allocation is a fundamental problem in distributed computing in which p asynchronous processes must execute a set of m tasks. Also known as writeall or doall, this problem been studied extensively, both independently and as a key building block for various distributed algorithms. In this paper, we break new ground on this classic problem: we introduce the ToDoTree concurrent data structure, which improves on the best known randomized and deterministic upper bounds. In the presence of an adaptive adversary, the randomized ToDoTree algorithm has O(m + p log p log 2 m) work complexity. We then show that there exists a deterministic variant of the ToDoTree algorithm with work complexity O(m+p log 5 m log 2 max(m, p)). For all values of m and p, our algorithms are within log factors of the Ω(m+p log p) lower bound for this problem. The key technical ingredient in our results is a new approach for analyzing concurrent executions against a strong adaptive scheduler. This technique allows us to handle the complex dependencies between the processes’ coin flips and their scheduling, and to tightly bound the work needed to perform subsets of the tasks. I.