Showing papers by "Ulrich Meyer published in 2000"
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TL;DR: The variegate spectrum of experimental results gives a good picture of the features of these priority queues, thus being helpful to anyone interested in the use of such data structures on very large data sets.
Abstract: In this paper we compare the performance of eight different priority queue implementations: four of them are explicitly designed to work in an external-memory setting, the others are standard internal-memory queues available in the LEDA library [Mehlhorn and Naher 1999]. Two of the external-memory priority queues are obtained by engineering known internal-memory priority queues with the aim of achieving effective performance on external storage devices (i.e., Radix heaps [Ahuja et al. 1990] and array heaps [Thorup 1996]). Our experimental framework includes some simple tests, like random sequences of insert or delete-minimum operations, as well as more advanced tests consisting of intermixed sequences of update operations and "application driven" update sequences originated by simulations of Dijkstra's algorithm on large graph instances. Our variegate spectrum of experimental results gives a good picture of the features of these priority queues, thus being helpful to anyone interested in the use of such data structures on very large data sets.
26 citations
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29 Aug 2000TL;DR: In this article, the authors present an algorithm for graphs where the ratio dc/Δ between the maximum weight of a shortest path dc and a "safe step width" Δ is not too large.
Abstract: In spite of intensive research, no work-efficient parallel algorithm for the single source shortest path problem is known which works in sublinear time for arbitrary directed graphs with non-negative edge weights. We present an algorithm that improves this situation for graphs where the ratio dc/Δ between the maximum weight of a shortest path dc and a "safe step width" Δ is not too large. We show how such a step width can be found efficiently and give several graph classes which meet the above condition, such that our parallel shortest path algorithm runs in sublinear time and uses linear work.Th e new algorithm is even faster than a previous one which only works for random graphs with random edge weights [10]. On those graphs our new approach is faster by a factor of Θ(log n/ log log n) and achieves an expected time bound of O(log2 n) using linear work.
20 citations
01 Jan 2000
TL;DR: An algorithm is presented that improves this situation for graphs where the ratio dc/Δ between the maximum weight of a shortest path dc and a "safe step width" Δ is not too large and achieves an expected time bound of O(log2 n) using linear work.
Abstract: In spite of intensive research, no work-efficient parallel algorithm for the single source shortest path problem is known which works in sublinear time for arbitrary directed graphs with non-negative edge weights. We present an algorithm that improves this situation for graphs where the ratio dc/Δ between the maximum weight of a shortest path dc and a "safe step width" Δ is not too large. We show how such a step width can be found efficiently and give several graph classes which meet the above condition, such that our parallel shortest path algorithm runs in sublinear time and uses linear work.Th e new algorithm is even faster than a previous one which only works for random graphs with random edge weights [10]. On those graphs our new approach is faster by a factor of Θ(log n/ log log n) and achieves an expected time bound of O(log2 n) using linear work.
15 citations