Optical clustering on a mesh-connected computer

In this paper, we present optimal parallel algorithms for optical clustering on a mesh-connected computer.Optical clustering is a clustering technique based on the principal of optical resolution, and is of particular interest in picture analysis. The algorithms we present are based on the application of parallel algorithms in computational geometry and graph theory. In particular, we show that given a setS ofN points in the Euclidean plane, the following problems can be solved in optimal time on a mesh-connected computer of sizeN.

Erläuterungen und Anwendungsbeispiel zum vfdb‐Leitfaden Ingenieurmethoden des Brandschutzes

Comment to the vfdb‐guidelines “Methods of fire safety engineering”. In the last eight years the vfdb Working Group 4 elaborated the Guidelines “Methods of fire safety engineering“. They shall give help to choose appropriate methods and input data for fire safety engineering in the framework of a fire safety concept. This paper explains the overall concept and the relations between the different chapters of the Guidelines. Safety objectives and related performance requirements are discussed in more detail because they are important for the choice of relevant fire scenarios and design criteria and appropriate calculation methods. The application of the Guidelines is demonstrated for a convention building which is investigated with respect to smoke control and fire protection of the roof construction.     

A Randomized Parallel Three-Dimensional Convex Hull Algorithm for Coarse-Grained Multicomputers

We present a randomized parallel algorithm for constructing the three-dimensional convex hull on a generic p-processor coarse-grained multicomputer with arbitrary interconnection network and n/p local memory per processor, where n/p ≥ p ^2+ε (for some arbitrarily small ε > 0). For any given set of n points in 3-space, the algorithm computes the three-dimensional convex hull, with high probability, in local computation time and O(1) communication phases with at most O(n/p) data sent/received by each processor. That is, with high probability, the algorithm computes the three-dimensional convex hull of an arbitrary point set in time , where Γ _n,p denotes the time complexity of one communication phase. The assumption n/p ≥ p ^2+ε implies a coarse-grained, limited parallelism, model which is applicable to most commercially available multiprocessors. In the terminology of the BSP model, our algorithm requires, with high probability, O(1) supersteps, synchronization period , computation cost , and communication cost O((n/p) g). Received October 30, 1995, and in revised form April 15, 1996, and in final form September 17, 1996.     

PnP: sequential, external memory, and parallel iceberg cube computation

We present “Pipe ’n Prune” (PnP), a new hybrid method for iceberg-cube query computation. The novelty of our method is that it achieves a tight integration of top-down piping for data aggregation with bottom-up a priori data pruning. A particular strength of PnP is that it is efficient for all of the following scenarios: (1) Sequential iceberg-cube queries, (2) External memory iceberg-cube queries, and (3) Parallel iceberg-cube queries on shared-nothing PC clusters with multiple disks. We performed an extensive performance analysis of PnP for the above scenarios with the following main results: In the first scenario PnP performs very well for both dense and sparse data sets, providing an interesting alternative to BUC and Star-Cubing. In the second scenario PnP shows a surprisingly efficient handling of disk I/O, with an external memory running time that is less than twice the running time for full in-memory computation of the same iceberg-cube query. In the third scenario PnP scales very well, providing near linear speedup for a larger number of processors and thereby solving the scalability problem observed for the parallel iceberg-cubes proposed by Ng et al. Research partially supported by the Natural Sciences and Engineering Research Council of Canada. A preliminary version of this work appeared in the International Conference on Data Engineering (ICDE’05).     

Computational geometry algorithms for the systolic screen

Adigitized plane of sizeM is a rectangular M × M array of integer lattice points called pixels. A M × M mesh-of-processors in which each processorP _ij represents pixel (i,j) is a natural architecture to store and manipulate images in ; such a parallel architecture is called asystolic screen. In this paper we consider a variety of computational-geometry problems on images in a digitized plane, and present optimal algorithms for solving these problems on a systolic screen. In particular, we presentO(M)-time algorithms for determining all contours of an image; constructing all rectilinear convex hulls of an image (peeling); solving the parallel and perspective visibility problem forn disjoint digitized images; and constructing the Voronoi diagram ofn planar objects represented by disjoint images, for a large class of object types (e.g., points, line segments, circles, ellipses, and polygons of constant size) and distance functions (e.g., allL _p metrics). These algorithms implyO(M)-time solutions to a number of other geometric problems: e.g., rectangular visibility, separability, detection of pseudo-star-shapedness, and optical clustering. One of the proposed techniques also leads to a new parallel algorithm for determining all longest common subsequences of two words.Research supported by the Naural Sciences and Engineering Research Council of Canada. With the Editor-in-Chief's permission, this paper was sent to the referees in a form which kept them unaware of the fact that the Guest Editor is one of the co-authors.     

Efficient External Memory Algorithms by Simulating Coarse-Grained Parallel Algorithms

External memory (EM) algorithms are designed for large-scale computational problems in which the size of the internal memory of the computer is only a small fraction of the problem size. Typical EM algorithms are specially crafted for the EM situation. In the past, several attempts have been made to relate the large body of work on parallel algorithms to EM, but with limited success. The combination of EM computing, on multiple disks, with multiprocessor parallelism has been posted as a challenge by the ACM Working Group on Storage I/ O for Large-Scale Computing. In this paper we provide a simulation technique which produces efficient parallel EM algorithms from efficient BSP-like parallel algorithms. The techniques obtained can accommodate one or multiple processors on the EM target machine, each with one or more disks, and they also adapt to the disk blocking factor of the target machine. When applied to existing BSP-like algorithms, our simulation technique produces improved parallel EM algorithms for a large number of problems.     

Shortest Paths in Time-Dependent FIFO Networks

In this paper, we study the time-dependent shortest paths problem for two types of time-dependent FIFO networks. First, we consider networks where the availability of links, given by a set of disjoint time intervals for each link, changes over time. Here, each interval is assigned a non-negative real value which represents the travel time on the link during the corresponding interval. The resulting shortest path problem is the time-dependent shortest path problem for availability intervals ( $\mathcal{TDSP}_{\mathrm{int}}$ ), which asks to compute all shortest paths to any (or all) destination node(s) d for all possible start times at a given source node s. Second, we study time-dependent networks where the cost of using a link is given by a non-decreasing piece-wise linear function of a real-valued argument. Here, each piece-wise linear function represents the travel time on the link based on the time when the link is used. The resulting shortest paths problem is the time-dependent shortest path problem for piece-wise linear functions ( $\mathcal{TDSP}_{\mathrm{lin}}$ ) which asks to compute, for a given source node s and destination d, the shortest paths from s to d, for all possible starting times. We present an algorithm for the $\mathcal{TDSP}_{\mathrm{lin}}$ problem that runs in time O((F _d +γ)(|E|+|V|log?|V|)) where F _d is the output size (i.e., number of linear pieces needed to represent the earliest arrival time function to d) and γ is the input size (i.e., number of linear pieces needed to represent the local earliest arrival time functions for all links in the network). We then solve the $\mathcal{TDSP}_{\mathrm{int}}$ problem in O(λ(|E|+|V|log?|V|)) time by reducing it to an instance of the $\mathcal{TDSP}_{\mathrm{lin}}$ problem. Here, λ denotes the total number of availability intervals in the entire network. Both methods improve significantly on the previously known algorithms.     

Efficient External Memory Algorithms by Simulating Coarse-Grained Parallel Algorithms

Abstract. External memory (EM) algorithms are designed for large-scale computational problems in which the size of the internal memory of the computer is only a small fraction of the problem size. Typical EM algorithms are specially crafted for the EM situation. In the past, several attempts have been made to relate the large body of work on parallel algorithms to EM, but with limited success. The combination of EM computing, on multiple disks, with multiprocessor parallelism has been posted as a challenge by the ACM Working Group on Storage I/ O for Large-Scale Computing. In this paper we provide a simulation technique which produces efficient parallel EM algorithms from efficient BSP-like parallel algorithms. The techniques obtained can accommodate one or multiple processors on the EM target machine, each with one or more disks, and they also adapt to the disk blocking factor of the target machine. When applied to existing BSP-like algorithms, our simulation technique produces improved parallel EM algorithms for a large number of problems.     

Parallelizing the Data Cube

This paper presents a general methodology for the efficient parallelization of existing data cube construction algorithms. We describe two different partitioning strategies, one for top-down and one for bottom-up cube algorithms. Both partitioning strategies assign subcubes to individual processors in such a way that the loads assigned to the processors are balanced. Our methods reduce inter processor communication overhead by partitioning the load in advance instead of computing each individual group-by in parallel. Our partitioning strategies create a small number of coarse tasks. This allows for sharing of prefixes and sort orders between different group-by computations. Our methods enable code reuse by permitting the use of existing sequential (external memory) data cube algorithms for the subcube computations on each processor. This supports the transfer of optimized sequential data cube code to a parallel setting.The bottom-up partitioning strategy balances the number of single attribute external memory sorts made by each processor. The top-down strategy partitions a weighted tree in which weights reflect algorithm specific cost measures like estimated group-by sizes. Both partitioning approaches can be implemented on any shared disk type parallel machine composed of p processors connected via an interconnection fabric and with access to a shared parallel disk array.We have implemented our parallel top-down data cube construction method in C++ with the MPI message passing library for communication and the LEDA library for the required graph algorithms. We tested our code on an eight processor cluster, using a variety of different data sets with a range of sizes, dimensions, density, and skew. Comparison tests were performed on a SunFire 6800. The tests show that our partitioning strategies generate a close to optimal load balance between processors. The actual run times observed show an optimal speedup of p.