Common parallelization strategy of topological operators on SMP machines

....................................................................................................................................................... 3 RÉSUMÉ ............................................................................................................................................................. 4 ACKNOWLEDGEMENTS / REMERCIEMENTS ............................................................................................ 5 PUBLICATIONS ................................................................................................................................................ 6 CONTENTS ........................................................................................................................................................ 8 LIST OF FIGURES ........................................................................................................................................... 10 LIST OF TABLES ............................................................................................................................................ 11 LIST OF DEFINITIONS ................................................................................................................................... 12 LIST OF ALGORITHMS ................................................................................................................................. 13 INTRODUCTION ............................................................................................................................................. 14 1.1 Context and motivations .................................................................................................................... 14 1.2 Contributions ..................................................................................................................................... 15 1.3 Report organization ........................................................................................................................... 17 PARALLELIZATION STRATEGY ................................................................................................................. 18 2.1 Lack of common parallelization strategy for topological operators .................................................. 19 2.2 Fundamental basis for parallelization ................................................................................................ 19 2.3 Classification of SD&M strategy ...................................................................................................... 22 2.4 SD&M strategy conception ............................................................................................................... 23 2.4.1 The splitting phase ..................................................................................................................... 24 2.4.2 Distribution phase ...................................................................................................................... 27 2.4.3 The Merging phase .................................................................................................................... 34 2.5 Conclusion ......................................................................................................................................... 36 TOPOLOGICAL WATERSHED...................................................................................................................... 37 3.1 Watershed transformations ................................................................................................................ 37 3.1.1 Watershed based on flooding .................................................................................................... 39 3.1.2 Watershed based on path-cost minimization ............................................................................. 42 3.1.3 Topological watershed ............................................................................................................... 47 3.1.4 Watershed transform based on local condition .......................................................................... 50 3.1.5 Watershed transform based on minimum spanning forest......................................................... 52 3.2 Classification of watershed algorithms .............................................................................................. 54 3.3 Construction of parallel topological watershed ................................................................................. 55 3.3.1 Basic notions and definitions ..................................................................................................... 56 3.3.2 Parallel stream computing ......................................................................................................... 57 pa st el -0 06 80 73 5, v er si on 1 20 M ar 2 01 2