Mixed-approach algorithms for transitive closure (extended abstract)

Jakobsson, Håkan

doi:10.1145/113413.113431

Cited by 16 publications

(10 citation statements)

References 18 publications

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“…In some cases, however, it is faster than other transitive closure algorithms. This is of interest since a conceivably small random sample of elements from each reachability set may be useful for some applications and, furthermore, an abundance of papers in the database literature are concerned with faster transitive closure algorithms for some families of graphs (e.g., Jakobsson gave faster algorithms for graphs with certain connectivity properties [13,14]; also see Dar [9] for an experimental comparison of the performance of different transitiveclosure algorithms).…”

Section: Further Applicationsmentioning

confidence: 99%

Size-Estimation Framework with Applications to Transitive Closure and Reachability

Cohen

1997

Journal of Computer and System Sciences

356

515

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Computing the transitive closure in directed graphs is a fundamental graph problem. We consider the more restricted problem of computing the number of nodes reachable from every node and the size of the transitive closure. The fastest known transitive closure algorithms run in O(min[mn, n 2.38 ]) time, where n is the number of nodes and m the number of edges in the graph. We present an O(m) time randomized (Monte Carlo) algorithm that estimates, with small relative error, the sizes of all reachability sets and the transitive closure. Another ramification of our estimation scheme is a O (m) time algorithm for estimating sizes of neighborhoods in directed graphs with nonnegative edge lengths. Our size-estimation algorithms are much faster than performing the respective explicit computations. ] 1997 Academic Press

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Section: Further Applicationsmentioning

confidence: 99%

Size-Estimation Framework with Applications to Transitive Closure and Reachability

Cohen

1997

Journal of Computer and System Sciences

356

515

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“…There have been other improvements on the running time for the all-pairs shortest paths problem for some special case graphs [2,10,15,16,17,18,19,22,26], but they all have worst-case time O(nE). Karger, Koller, and Phillips [19] show that Ω(nE) is a lower bound for directed graphs on the running time of any algorithm which is "pathcomparison based," which is evidence that it is hard to improve exact algorithms with this approach.…”

Section: 1mentioning

confidence: 99%

Near-Linear Time Construction of Sparse Neighborhood Covers

Awerbuch

Berger

Cowen³

et al. 1998

SIAM J. Comput.

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Abstract. This paper introduces a near-linear time sequential algorithm for constructing a sparse neighborhood cover. This implies analogous improvements (from quadratic to near-linear time) for any problem whose solution relies on network decompositions, including small edge cuts in planar graphs, approximate shortest paths, and weight-and distance-preserving graph spanners. In particular, an O(log n) approximation to the k-shortest paths problem on an n-vertex, E-edge graph is obtained that runs inÕ (n + E + k) time.

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“…The previous algorithms compute tuples from different source vertices at the same time, whereas a more parsimonious usage of memory can be achieved by computing the paths that originate from one source vertex one at the time [15].…”

Section: B Non-linear Tc Rules and The Smart Algorithmmentioning

confidence: 99%

Main memory evaluation of recursive queries on multicore machines

Yang

Zaniolo

2014

2014 IEEE International Conference on Big Data (Big Data)

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Supporting iteration and/or recursion for advanced big data analytics requires reexamination of classical algorithms on modern computing environments. Several recent studies have focused on the implementation of transitive closure in multi-node clusters. Algorithms that deliver optimal performance on multinode clusters are hardly optimal on multicore machines. We present an experimental study on finding efficient main memory recursive query evaluation algorithms on modern multi-core machines. We review SEMINAIVE, SMART and a pair of single-source closure (SSC) algorithms. We also propose a new hybrid SSC algorithm, named SSC12, which combines two previously known SSC algorithms. We implement these algorithms on a multicore shared memory machine, and compare their memory utilization, speed and scalability on synthetic and real-life datasets. Our experiments show that, on multicore machines, the surprisingly simple SSC12 is the only transitive-closure algorithm that is consistently fast and memory-efficient on all test graphs.

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Mixed-approach algorithms for transitive closure (extended abstract)

Cited by 16 publications

References 18 publications

Size-Estimation Framework with Applications to Transitive Closure and Reachability

Size-Estimation Framework with Applications to Transitive Closure and Reachability

Near-Linear Time Construction of Sparse Neighborhood Covers

Main memory evaluation of recursive queries on multicore machines

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