Showing papers by "Ulrich Meyer published in 1998"

A Parallelization of Dijkstra's Shortest Path Algorithm

Abstract: The single source shortest path (SSSP) problem lacks parallel solutions which are fast and simultaneously work-efficient. We propose simple criteria which divide Dijkstra's sequential SSSP algorithm into a number of phases, such that the operations within a phase can be done in parallel. We give a PRAM algorithm based on these criteria and analyze its performance on random digraphs with random edge weights uniformly distributed in [0,1]. We use the G (n, d/n) model: the graph consists of n nodes and each edge is chosen with probability d/n. Our PRAM algorithm needs O(n 1/3 log n) log n) time and O (n log n+dn) work with high probability (whp). We also give extensions to external memory computation. Simulations show the applicability of our approach even on non-random graphs.

Delta-Stepping: A Parallel Single Source Shortest Path Algorithm

Abstract: In spite of intensive research, little progress has been made towards fast and work-efficient parallel algorithms for the single source shortest path problem. Our Δ-stepping algorithm, a generalization of Dial's algorithm and the Bellman-Ford algorithm, improves this situation at least in the following "average-case" sense: For random directed graphs with edge probability d/n and uniformly distributed edge weights a PRAM version works in expected time O(log3 n/ log log n) using linear work. The algorithm also allows for efficient adaptation to distributed memory machines. Implementations show that our approach works on real machines. As a side effect, we get a simple linear time sequential algorithm for a large class of not necessarily random directed graphs with random edge weights.

$\Delta$-Stepping: A Parallel Single Source Shortest Path Algorithm

Abstract: In spite of intensive research, little progress has been made towards fast and work-efficient parallel algorithms for the single source shortest path problem. Our Δ-stepping algorithm, a generalization of Dial's algorithm and the Bellman-Ford algorithm, improves this situation at least in the following "average-case" sense: For random directed graphs with edge probability d/n and uniformly distributed edge weights a PRAM version works in expected time O(log3 n/ log log n) using linear work. The algorithm also allows for efficient adaptation to distributed memory machines. Implementations show that our approach works on real machines. As a side effect, we get a simple linear time sequential algorithm for a large class of not necessarily random directed graphs with random edge weights.

Randomized external-memory algorithms for some geometric problems

Abstract: We show that the well-known random incremental constructlon of Clarkson and Shor [14] can be adapted via gradations to provide efficient external-memory algorithms for some geomctric problems. In particular, as the main result, we obtain an optimal randomized algorithm for the problem of computing the trapezoidal decomposition determined by a set of N line scgmcnts in the plane with K pairwise intersections, that requires G($$ logMjB Q + 5) expected disk accesses (I/OS), where M is the size of the available internal memory and B is the size of the block transfer. The approach is sufficiently general to obtain algorithms for the problems of 2-d and 3-d convex hulls, 2-d abstract Voronoi diagrams and batched point location in a planar subdivision, which require an optimal expected number of I/OS and are olmplcr than the ones previously known. The results extend to a external-memory model with multiple disks.

A Parallelization of Dijkstra's Shortest Path Algorithm

Abstract: The single source shortest path (SSSP) problem lacks parallel solutions which are fast and simultaneously work-efficient. We propose simple criteria which divide Dijkstra's sequential SSSP algorithm into a number of phases, such that the operations within a phase can be done in parallel. We give a PRAM algorithm based on these criteria and analyze its performance on random digraphs with random edge weights uniformly distributed in [0,1]. We use the G (n, d/n) model: the graph consists of n nodes and each edge is chosen with probability d/n. Our PRAM algorithm needs O(n 1/3 log n) log n) time and O (n log n+dn) work with high probability (whp). We also give extensions to external memory computation. Simulations show the applicability of our approach even on non-random graphs.

Time-independent gossiping on full-port tori

Abstract: Near-optimal gossiping algorithms are given for twoand higher dimensional tori. It is assumed that the amount of data each PU contributes is so large that start-up time may be neglected. For twodimensional tori, a previous algorithm achieved optimality in an intricate way, with a time-dependent routing pattern. In all steps of our algorithms, the PUs forward the received packets in the same way.

Gossiping Large Packets on Full-Port Tori

Abstract: Near-optimal gossiping algorithms are given for two- and higher dimensional tori. It is assumed that the amount of data each PU is contributing is so large, that start-up time may be neglected. For two-dimensional tori, an earlier algorithm achieved optimality in an intricate way, with a time-dependent routing pattern. In our algorithms, in all steps, the PUs forward the received packets in the same way.

Gossiping Large Packets on Full-Port Tori

Abstract: Near-optimal gossiping algorithms are given for two- and higher dimensional tori. It is assumed that the amount of data each PU is contributing is so large, that start-up time may be neglected. For two-dimensional tori, an earlier algorithm achieved optimality in an intricate way, with a time-dependent routing pattern. In our algorithms, in all steps, the PUs forward the received packets in the same way.