Average-case complexity of single-source shortest-paths algorithms: lower and upper bounds

Meyer, Ulrich

doi:10.1016/s0196-6774(03)00046-4

Cited by 35 publications

(19 citation statements)

References 58 publications

(109 reference statements)

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“…As a counterexample, the selection sort algorithm can be given; its behavior does not depend on the input data structure. Furthermore, other types of algorithms can be indicated: a special group is graph algorithms (for example, spanning tree algorithms (Kruskal's algorithm, Prim's algorithm, Boruvka's algorithm) with all included modifications, especially if graphs have special features (are dense, edge weights are integers (see [29])); Dijkstra's or Bellman-Ford methods for shortest paths with improvements in representation of graphs stored in different data structures (see, for example, [30])).…”

Section: Discussionmentioning

confidence: 99%

Selected Remarks about Computer Processing in Terms of Flow Control and Statistical Mechanics

Strzałka

2016

Entropy

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Despite the fact that much has been said about processing in computer science, it seems that there is still much to do. A classical approach assumes that the computations done by computers are a kind of mathematical operation (calculations of functions values) and have no special relations to energy transformation and flow. However, there is a possibility to get a new view on selected topics, and as a special case, the sorting problem is presented; we know many different sorting algorithms, including those that have complexity equal to O(n lg(n)), which means that this problem is algorithmically closed, but it is also possible to focus on the problem of sorting in terms of flow control, entropy and statistical mechanics. This is done in relation to the existing definitions of sorting, connections between sorting and ordering and some important aspects of computer processing understood as a flow that are not taken into account in many theoretical considerations in computer science. The proposed new view is an attempt to change the paradigm in the description of algorithms' performance by computational complexity and processing, taking into account the existing references between the idea of Turing machines and their physical implementations. This proposal can be expressed as a physics of computer processing; a reference point to further analysis of algorithmic and interactive processing in computer systems.

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Section: Discussionmentioning

confidence: 99%

Selected Remarks about Computer Processing in Terms of Flow Control and Statistical Mechanics

Strzałka

2016

Entropy

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“…If edge weight are integral and bounded by a small constant, Dial's implementation [5] with an array of lists ("buckets") provides a priority queue where all operations take constant time. An extension with average linear complexity for uniformly distributed edge weights is presented in [9,26]. One might argue however, that the better a speed-up techniques works, the smaller the search front is, and the less important the priority queue is.…”

Section: Shortest Path Problemmentioning

confidence: 99%

Speed-Up Techniques for Shortest-Path Computations

Wagner

Willhalm

Stacs 2007

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Abstract. During the last years, several speed-up techniques for Dijkstra's algorithm have been published that maintain the correctness of the algorithm but reduce its running time for typical instances. They are usually based on a preprocessing that annotates the graph with additional information which can be used to prune or guide the search. Timetable information in public transport is a traditional application domain for such techniques. In this paper, we provide a condensed overview of new developments and extensions of classic results. Furthermore, we discuss how combinations of speed-up techniques can be realized to take advantage from different strategies.

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“…At present, CUDA has become the mainstream environment in the field of GPU. With the improving performance and programmability on GPU, it has evolved into general processor with high parallelism, strong computing ability and high DRAM bandwidth [5].…”

Section: Introductionmentioning

confidence: 99%

A Synchronization Mechanism between CUDA Blocks for GPU

Wang¹,

Zhang²,

Wang³

et al. 2017

Proceedings of the 2017 2nd International Conference on Control, Automation and Artificial Intelligence (CAAI 2017)

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Abstract-GPU(Graphic Processing Unit) provides a promising solution with massive threads and its advantage is high performance computing. The emergence of CUDA(Compute Unified Device Architecture) opens the door of using GPU's powerful computing power. However, because of the limitation of CUDA itself, direct communication is not supported between SMs(streaming multiprocessors) on GPU. It is time-consuming by atomic operation or barrier synchronization. A synchronization mechanism has been proposed in this paper, that is, on the premise of result available, the times of kernel launched should be reduced. Each kernel launched, it should be computed enough on GPU, the results back to the CPU. Based on SSSP, the validity of this method is illustrated by delta-stepping. For facebook dataset, compared with atomic operation, the speedup ratio is about 1.8. For New York map dataset, compared with atomic operation and barrier synchronization, the speedup ratio is about 9.3 and 1.7 separately.

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Average-case complexity of single-source shortest-paths algorithms: lower and upper bounds

Cited by 35 publications

References 58 publications

Selected Remarks about Computer Processing in Terms of Flow Control and Statistical Mechanics

Selected Remarks about Computer Processing in Terms of Flow Control and Statistical Mechanics

Speed-Up Techniques for Shortest-Path Computations

A Synchronization Mechanism between CUDA Blocks for GPU

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