Scalable algorithms for bichromatic line segment intersection problems on coarse grained multicomputers

International audienceWe present output-sensitive scalable parallel algorithms for bichromatic line segment intersection problems for the coarse grained multicomputer model. Under the assumption that n≥p^2, where n is the number of line segments and p the number of processors, we obtain an intersection counting algorithm with a time complexity of O( (n log n log p)/p + Ts(n log p,p) ), where Ts(m, p) is the time used to sort m items on a p processor machine. The first term captures the time spent in sequential computation performed locally by each processor. The second term captures the interprocessor communication time. An additional O(k/p) time in sequential computation is spent on the reporting of the k intersections. As the sequential time complexity is O(n log n) for counting and an additional time O(k) for reporting, we obtain a speedup of p/log p in the sequential part of the algorithm. The speedup in the communication part obviously depends on the underlying architecture. For example for a hypercube it ranges between p/log^2p and p/log p depending on the ratio of n and p. As the reporting does not involve more interprocessor communication than the counting, the algorithm achieves a full speedup of p for k≥ O(max(n log n log p, n log^3 p)) even on a hypercube

Visibility-Related Problems on Parallel Computational Models

Visibility-related problems find applications in seemingly unrelated and diverse fields such as computer graphics, scene analysis, robotics and VLSI design. While there are common threads running through these problems, most existing solutions do not exploit these commonalities. With this in mind, this thesis identifies these common threads and provides a unified approach to solve these problems and develops solutions that can be viewed as template algorithms for an abstract computational model. A template algorithm provides an architecture independent solution for a problem, from which solutions can be generated for diverse computational models. In particular, the template algorithms presented in this work lead to optimal solutions to various visibility-related problems on fine-grain mesh connected computers such as meshes with multiple broadcasting and reconfigurable meshes, and also on coarse-grain multicomputers. Visibility-related problems studied in this thesis can be broadly classified into Object Visibility and Triangulation problems. To demonstrate the practical relevance of these algorithms, two of the fundamental template algorithms identified as powerful tools in almost every algorithm designed in this work were implemented on an IBM-SP2. The code was developed in the C language, using MPI, and can easily be ported to many commercially available parallel computers

Scalable algorithms for bichromatic line segment intersection problems on coarse grained multicomputers

Programme 4 : robotique, image et visionSIGLEAvailable at INIST (FR), Document Supply Service, under shelf-number : 14802 E, issue : a.1993 n.1882 / INIST-CNRS - Institut de l'Information Scientifique et TechniqueFRFranc

Scalable Algorithms For Bichromatic Line Segment Intersection Problems On Coarse Grained Multicomputers

We present output-sensitive scalable parallel algorithms for bichromatic line segment intersection problems for the coarse grained multicomputer model. Under the assumption that n p 2 , where n is the number of line segments and p the number of processors, we obtain an intersection counting algorithm with a time complexity of O( n log n log p p + T s (n log p; p)), where T s (m; p) is the time used to sort m items on a p processor machine. The first term captures the time spent in sequential computation performed locally by each processor. The second term captures the interprocessor communication time. An additional O( k p ) time in sequential computation is spent on the reporting of the k intersections. As the sequential time complexity is O(n log n) for counting and an additional time O(k) for reporting, we obtain a speedup of p log p in the sequential part of the algorithm. The speedup in the communication part obviously depends on the underlying architecture. For example for a hypercube it ranges between p log 2 p and p log p depending on the ratio of n and p. As the reporting does not involve more interprocessor communication than the counting, the algorithm achieves a full speedup of p for k O(max(n log n log p; n log 3 p)) even on a hypercube

Efficient algorithms for new computational models

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2003.Includes bibliographical references (p. 155-163).This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Advances in hardware design and manufacturing often lead to new ways in which problems can be solved computationally. In this thesis we explore fundamental problems in three computational models that are based on such recent advances. The first model is based on new chip architectures, where multiple independent processing units are placed on one chip, allowing for an unprecedented parallelism in hardware. We provide new scheduling algorithms for this computational model. The second model is motivated by peer-to-peer networks, where countless (often inexpensive) computing devices cooperate in distributed applications without any central control. We state and analyze new algorithms for load balancing and for locality-aware distributed data storage in peer-to-peer networks. The last model is based on extensions of the streaming model. It is an attempt to capture the class of problems that can be efficiently solved on massive data sets. We give a number of algorithms for this model, and compare it to other models that have been proposed for massive data set computations. Our algorithms and complexity results for these computational models follow the central thesis that it is an important part of theoretical computer science to model real-world computational structures, and that such effort is richly rewarded by a plethora of interesting and challenging problems.by Jan Matthias Ruhl.Ph.D