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Pregel: A system for largescale graph processing
 IN SIGMOD
, 2010
"... Many practical computing problems concern large graphs. Standard examples include the Web graph and various social networks. The scale of these graphs—in some cases billions of vertices, trillions of edges—poses challenges to their efficient processing. In this paper we present a computational model ..."
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Many practical computing problems concern large graphs. Standard examples include the Web graph and various social networks. The scale of these graphs—in some cases billions of vertices, trillions of edges—poses challenges to their efficient processing. In this paper we present a computational model suitable for this task. Programs are expressed as a sequence of iterations, in each of which a vertex can receive messages sent in the previous iteration, send messages to other vertices, and modify its own state and that of its outgoing edges or mutate graph topology. This vertexcentric approach is flexible enough to express a broad set of algorithms. The model has been designed for efficient, scalable and faulttolerant implementation on clusters of thousands of commodity computers, and its implied synchronicity makes reasoning about programs easier. Distributionrelated details are hidden behind an abstract API. The result is a framework for processing large graphs that is expressive and easy to program.
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
Solving the atmostonce problem with nearly optimal effectiveness
 Theoretical Computer Science
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The Strong AtMostOnce Problem
"... Abstract. The atmostonce problem in shared memory asks for the completion of a number of tasks by a set of independent processors while adhering to “at most once ” semantics. Atmostonce algorithms are evaluated in terms of effectiveness, which is a measure that expresses the total number of tas ..."
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Abstract. The atmostonce problem in shared memory asks for the completion of a number of tasks by a set of independent processors while adhering to “at most once ” semantics. Atmostonce algorithms are evaluated in terms of effectiveness, which is a measure that expresses the total number of tasks completed atmostonce in the worst case. Motivated by the lack of deterministic solutions with high effectiveness, we study the feasibility of (a close variant of) this problem. The strong at most once problem is solved by an atmostone algorithm when all tasks are performed if no participating processes crash during the execution of the algorithm. We prove that the strong atmostonce problem has consensus number 2. This explains, via impossibility, the lack of waitfree deterministic solutions with high effectiveness for the at most once problem using only read/write atomic registers. We then present the first kadaptive effectiveness optimal randomized solution for the strong atmostonce problem, that has optimal expected work for a nontrivial number of participating processes. Our solution also provides the first kadaptive randomized solution for the WriteAll problem, a dual problem to atmostonce. 1