Parallel Algorithms for Irregular Problems: State of the Art

Transcription

1 Parallel Algorithms for Irregular Problems: State of the Art

2 Parallel Algorithms for Irregular Problems: State of the Art Edited by Manso Ferreira LIP, Lyon and Jose D. P. Rolim Unwer~ of Geneva SPRINGER-SCIENCE+BUSINESS MEDIA, B.V.

3 Library of Congress Cataloging-in-Publication Data Parallel algor1thms for 1rregular problems state of the art I edited by Afonso Ferre1ra, Jose D.P. Rol1m. p. cm. Papers from a workshop and summer school held 1n Geneva 1n Includes bibl1ograph1cal references. ISBN ISBN (ebook) DOI / Parallel process1ng (Electron1c computers) 2. Computer algorlthms. I. Ferre1ra, Afonso. II. Rolim, Jose D. P. QA76.58.P dc ISBN Printed on acid-free paper All Rights Reserved 1995 Springer Science+Business Media Dordrecht Originally published by Kluwer Academic Publishers in 1995 No part of the material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording or by any information storage and retrieval system, without written permission from the copyright owner,

4 CONTENTS PREFACE Xl Part I SCIENTIFIC COMPUTATION 1 1 PARALLELIZATION STRATEGIES FOR MATRIX ASSEMBLY IN FINITE ELEMENT METHODS Jorn Behrens Parallelization by Color Indexing 5 3 Parallelization by Index-Array Mapping 8 4 Experimental Results 10 5 Conclusion APPENDIX A Detailed Description and Plausibility ofthe Color Indexing Method 17 APPENDIX B Tables of Timing Results 23 2 A PARALLELISABLE ALGORITHM FOR PARTITIONING UNSTRUCTURED MESHES C. Walshaw, M. Cross, M. Everett and S. Johnson 2 Notation and Definitions 3 The Initial Partition 4 The Parallel Optimisation Method 5 Clustering: Reducing the Problem Size 6 Experimental Results v

5 VI PARALLEL ALGORITHMS FOR IRREGULAR PROBLEMS 7 Conclusion PLUMP: PARALLEL LIBRARY FOR UNSTRUCTURED MESH PROBLEMS Ivan Beg, Wu Ling, Andreas Milller, Piotr Przybyszewski, Roland Rilhl and William Sawyer HPF /PST Support for Unstructured Problems 49 3 Design of Library 52 4 PLUMP Specification 53 5 Example Applications 63 6 Conclusions and Future Work PARALLELIZING VISION COMPUTATIONS ON CM-5: ALGORITHMS AND EXPERIENCES Viktor K. Prasanna and Cho-Li Wang 2 Representative Vision Tasks 3 A Model of CM-5 4 Scalable Parallel Algorithms 5 Implementation Details and Experimental Results 6 Concluding Remarks Part II DISCRETE OPTIMIZATION SCALABLE PARALLEL ALGORITHMS FOR UNSTRUCTURED PROBLEMS Vip in Kumar, Ananth Grama, Anshul Gupta, and George }(a ryp is Parallel Algorithms for Discrete Optimization Highly Parallel Direct Solvers for Sparse Linear Systems

6 Contents VB 6 A PARALLEL GRASP IMPLEMENTATION FOR THE QUADRATIC ASSIGNMENT PROBLEM P.M. Pardalos, L.S. Pitsoulis and M. G. C. Resende Parallel Exact Algorithms for the QAP Parallel Heuristics for the QAP Computational Results Concluding Remarks CONCURRENT DATA STRUCTURES FOR TREE SEARCH ALGORITHMS Bertrand Le Cun, Catherine Roucairol 2 Tree Search Algorithms 3 Concurrent Access to Global Data Structures 4 Best First Branch and Bound Algorithm 5 Concurrent Data Structure for Parallel A * 6 Concluding Remarks and Future Works A DISTRIBUTED IMPLEMENTATION OF ASYNCHRONOUS PARALLEL BRANCH AND BOUND Ricardo Correa and Afonso Ferreira Preliminaries on Sequential B&B Modeling Synchronous and Asynchronous Parallel B&B A Distributed Implementation of the Synchronous Model A Distributed Implementation of the Asynchronous Model Experimental Results and Comparisons Conclusions and Further Research

7 Vlll PARALLEL ALGORITHMS FOR IRREGULAR PROBLEMS 9 EXPERIMENTS WITH A PARALLEL SYNCHRONIZED BRANCH AND BOUND ALGORITHM Claude G. Diderich and Marc Gengler The Synchronized Parallel Branch and Bound Algorithm The Mixed Integer Programming Problem Experimental Results Open Problems and Conclusion PARALLEL LOCAL SEARCH AND JOB SHOP SCHEDULING M.G.A. Verhoeven, E.H.L. Aarts Local Search Job Shop Scheduling Local Search and Job Shop Scheduling Parallel Local Search Parallel Local Search for Job Shop Scheduling Discussion A RANDOMIZED PARALLEL SEARCH STRATEGY A. Clementi, L. Kucera and J. D. P. Rolim Preliminaries Random Graphs with Constant Edge Probability Other Edge Probability Functions Conclusions

8 Contents IX 12 A PARALLEL APPROXIMATION SCHEMA FOR SYMMETRIC LINEAR ASSIGNMENT PROBLEM Erik Urland and Definitions 2 Auction Algorithm 3 Parallel Approach 4 Computational Results 5 Approximation Schema Part III TOOLS FOR AUTOMATIC PARALLELIZATION 13 APPLICATIONS OF GRAPH SCHEDULING TECHNIQUES IN PARALLELIZING IRREGULAR SCIENTIFIC COMPUTATION Apostolos Gerasoulis J Jia Jiao and Tao Yang 2 Task Computation Model and Scheduling 3 The Run Time Method for Executing a Schedule 4 Solving Irregular Problems 5 Conclusions 6 Acknowledgements 14 ATREDIA: A MAPPING ENVIRONMENT FOR DYNAMIC TREE-STRUCTURED PROBLEMS Angela Sodan 2 Comparison with other Research 3 General Features of the Environment 4 Granularity Control 5 Profiling and Evaluation of Data 6 System and Application Models 7 Cost Functions

9 x PARALLEL ALGORITHMS FOR IRREGULAR PROBLEMS 8 Load Balancing and Scheduling 9 Decision Rules for Selection and Configuration 10 Experimental Results 11 Summary and Discussion 15 REGULARISING TRANSFORMATIONS FOR INTEGRAL DEPENDENCIES Graham M. Megson and Lucia Rapanotti 2 Basic Concepts 3 Integral Recurrence Equations 4 Localisation of Integral Recurrence Equations 5 The Knapsack Problem 6 Conclusions 16 SOME STRATEGIES FOR LOAD BALANCING Claude G. Diderich and Marc Gengler 2 Analyzing the Imbalance 3 Local Policies 4 Global Policies 5 Conclusion

10 PREFACE Efficient parallel solutions have been found to many problems. Some of these solutions can be automatically obtained from sequential programs using compilers. However, there still exists a large class of problems, known as irregular problems, that lack efficient solutions. Aiming at fostering the cooperation among practitioners and theoreticians of the field, the workshop and summer school on Parallel Algorithms for Irregularly Structured Problems - IRREG ULAR 94 - was organized in Geneva in 1994, addressing issues related to deriving efficient solutions to irregular problems. Evidently, the first question to be answered is "what are irregular problems?". Therefore, during IRREGULAR 94 we brought up all participants in a joint effort to answer it. What follows is an informal synthesis of what was said. A regular (or iso-ergo tic) algorithm is such that its dependence (or task) graph is independent of the instance data, meaning that the work accomplished by the algorithm is always the same, up to a (small) constant. On the other hand, the dependence graph of non-regular algorithms (also proposed was ataxidi algorithms) varies according to the input data, implying that the task scheduling cannot be evenly distributed beforehand in a parallel setting. An irregular problem is then characterized by the fact that there are ataxidi algorithms that execute faster than iso-ergo tic ones for the same instances in parallel. Of course, the quality of ataxidi algorithms is closely connected to its nonregularity. Complex choices are made concerning data-structuring techniques used to improve their sequential complexity, making their parallel versions very difficult implement without advanced dynamic load balancing strategies. Interest in irregular problems is growing throughout the world. There is a new SIG from IFIP, whose main activity is to coordinate the IRREGULAR series. Also, one of the main research topics within the HeM project SCOOP - Solving Combinatorial Optimization Problems in Parallel is how to cope with Xl

11 Xll PARALLEL ALGORITHMS FOR IRREGULAR PROBLEMS the irregularity in such problems. Finally, some French laboratories are involved in a project, named Stratageme, which addresses related problems. We were glad to see that attendance at IRREGULAR 94 was larger than expected, showing that we were not alone considering irregular problems as the key to massive parallelism. Hence, we decided to ask speakers to contribute to the present book, in order to lay a solid foundation where researchers world wide could build the theory and practice of parallel irregular applications. We tried to give the reader an overview of the main issues arising in the field. Therefore, this book is divided into three parts. The first one deals with scientific computation, covering different topics ranging from finite element methods to computer vision. The second part gathers research results on discrete optimization, mainly based on new techniques for parallel branch and bound. Last but not least, we show some important steps towards the development of tools for automatic parallelization. We hope that one day end-users will have at their disposal such tools that could efficiently parallelize even irregular problems. For more on this issue, rendez-vous a Lyon, France, in September 1995, for IRREGULAR 95. Afonso Ferreira, Jose" Rolim