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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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Cited by 170 (0 self)
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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.
Efficient Algorithms for Solving Static HamiltonJacobi Equations
, 2003
"... Consider the eikonal equation, = 1. If the initial condition is u = 0 on a manifold, then the solution u is the distance to the manifold. We present a new algorithm for solving this problem. More precisely, we present an algorithm for computing the closest point transform to an explicitly described ..."
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Cited by 48 (6 self)
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Consider the eikonal equation, = 1. If the initial condition is u = 0 on a manifold, then the solution u is the distance to the manifold. We present a new algorithm for solving this problem. More precisely, we present an algorithm for computing the closest point transform to an explicitly described manifold on a rectilinear grid in low dimensional spaces. The closest point transform finds the closest point on a manifold and the Euclidean distance to a manifold for all the points in a grid (or the grid points within a specified distance of the manifold). We consider manifolds composed of simple geometric shapes, such as, a set of points, piecewise linear curves or triangle meshes. The algorithm computes the closest point on and distance to the manifold by solving the eikonal equation = 1 by the method of characteristics. The method of characteristics is implemented efficiently with the aid of computational geometry and polygon/polyhedron scan conversion. Thus the method is named the characteristic/scan conversion algorithm. The computed distance is accurate to within machine precision. The computational complexity of the algorithm is linear in both the number of grid points and the complexity of the manifold. Thus it has optimal computational complexity. The algorithm is easily adapted to sharedmemory and distributedmemory concurrent algorithms. Many query problems...
A New Efficient Algorithm for Solving the Simple Temporal Problem
 In Proc. of Int. Syp. on Temporal Representation and Reasoning
, 2003
"... In this paper we propose a new efficient algorithm, the STPsolver, for computing the minimal network of the Simple Temporal Problem (STP). This algorithm achieves high performance by exploiting a topological property of the constraint graph (i.e., triangulation) and a semantic property of the const ..."
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Cited by 28 (4 self)
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In this paper we propose a new efficient algorithm, the STPsolver, for computing the minimal network of the Simple Temporal Problem (STP). This algorithm achieves high performance by exploiting a topological property of the constraint graph (i.e., triangulation) and a semantic property of the constraints (i.e., convexity) in light of the results reported by Bliek and SamHaroud [1], which were presented for general CSPs and have not yet been applied to temporal networks. Importantly, we design the constraint propagation in STPsolver to operate on triangles instead of operating on edges and implicitly guarantee the decomposition of the constraint graph according to its articulation points. We also provide extensive empirical evaluations of all known algorithms for solving the STP on sets of randomly generated problems. Our experiments demonstrate significant improvements of STPsolver, in terms of number of constraint checks and CPU time, over previously reported algorithms such as the FloydWarshall algorithm (FW) [5; 8], DirectedPath Consistency (DPC) [8], and Partial PathConsistency (PPC) [1]. 2
Dijkstra’s algorithm with Fibonacci heaps: An executable description
 in CHR. In 20th Workshop on Logic Programming (WLP’06
, 2006
"... Abstract. We construct a readable, compact and efficient implementation of Dijkstra’s shortest path algorithm and Fibonacci heaps using Constraint Handling Rules (CHR), which is increasingly used as a highlevel rulebased generalpurpose programming language. We measure its performance in different ..."
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Cited by 18 (11 self)
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Abstract. We construct a readable, compact and efficient implementation of Dijkstra’s shortest path algorithm and Fibonacci heaps using Constraint Handling Rules (CHR), which is increasingly used as a highlevel rulebased generalpurpose programming language. We measure its performance in different CHR systems, investigating both the theoretical asymptotic complexity and the constant factors realized in practice. 1
A Generalization of Binomial Queues
 Information Processing Letters
, 1996
"... We give a generalization of binomial queues involving an arbitrary sequence (mk )k=0;1;2;::: of integers greater than one. Different sequences lead to different worst case bounds for the priority queue operations, allowing the user to adapt the data structure to the needs of a specific application. ..."
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Cited by 2 (0 self)
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We give a generalization of binomial queues involving an arbitrary sequence (mk )k=0;1;2;::: of integers greater than one. Different sequences lead to different worst case bounds for the priority queue operations, allowing the user to adapt the data structure to the needs of a specific application. Examples include the first priority queue to combine a sublogarithmic worst case bound for Meld with a sublinear worst case bound for Delete min. Keywords: Data structures; Meldable priority queues. 1 Introduction The binomial queue, introduced in 1978 by Vuillemin [14], is a data structure for meldable priority queues. In meldable priority queues, the basic operations are insertion of a new item into a queue, deletion of the item having minimum key in a queue, and melding of two queues into a single queue. The binomial queue is one of many data structures which support these operations at a worst case cost of O(logn) for a queue of n items. Theoretical [2] and empirical [9] evidence i...
Experiments With the Auction Algorithm for the Shortest Path Problem.
, 1997
"... The auction approach for the shortest path problem as introduced by Bertsekas is tested experimentally. Parallel algorithms using the auction approach are developed and tested. Both the sequential and parallel auction algorithms perform significantly worse than a stateoftheart Dijkstralike refer ..."
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Cited by 1 (0 self)
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The auction approach for the shortest path problem as introduced by Bertsekas is tested experimentally. Parallel algorithms using the auction approach are developed and tested. Both the sequential and parallel auction algorithms perform significantly worse than a stateoftheart Dijkstralike reference algorithm. 1 Introduction The shortest path problem is one of the classical problems in Operations Research. One usually classifies shortest path algorithms into one of two groups: the labelsetting algorithms (Dijkstralike) and the labelcorrecting algorithms (BellmanFordlike) . A recent approach to solving shortest path problems is the auction algorithm proposed by Bertsekas in [Ber91]. In [PS91] and [BPS92] the performance of the auction algorithm is enhanced by the use of graph reduction, thereby reducing the worstcase timecomplexity from pseudopolynomial to strongly polynomial. Here we introduce the improved graph reduction scheme, which allows for additional reduction of th...
A Note on the Practical Performance of the Auction Algorithm for Shortest Paths
, 1997
"... The performance of the auction algorithms for the shortest paths has been investigated in four papers with differing conclusions. In the following I report a series of experiments with the code from the two most recent papers. The experiments clearly show that the auction algorithm is inferior to st ..."
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The performance of the auction algorithms for the shortest paths has been investigated in four papers with differing conclusions. In the following I report a series of experiments with the code from the two most recent papers. The experiments clearly show that the auction algorithm is inferior to stateoftheart shortest paths algorithms Keywords: shortest path problem, auction algorithm, performance results. 1 Introduction The (sequential) auction algorithms for the shortest path problem have been the subject of experiments which have been reported in at least five papers. The first paper [Ber91] introduced the auction algorithm for the shortest paths. This algorithm had pseudopolynomial timecomplexity. The paper also introduced the concepts of best and secondbest neighbour; improvements that enhanced the practical performance. In [PS91] graph reduction was introduced for the first time in the auction algorithm (here we call it simple reduction). This resulted in a polynomial au...
Models and Algorithms for Shortest Paths in a Time Dependent Network
"... Abstract The shortest path problem in the time dependent network is an important extension of the classical shortest path problem and has been widely applied in real life. It is known as nonlinear and NPhard. Therefore, the algorithms of the classical shortest path are incapable to solve this probl ..."
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Abstract The shortest path problem in the time dependent network is an important extension of the classical shortest path problem and has been widely applied in real life. It is known as nonlinear and NPhard. Therefore, the algorithms of the classical shortest path are incapable to solve this problem. In this paper, the models of the shortest path problem in the time dependent network are formulated and algorithms are designed for solving the proposed models. Finally, a numerical example is given.