Graph Partitioning: A Heuristic Procedure to Partition Network Graphs

...................................................................................iii LIST OF FIGURES...........................................................................................iv INTRODUCTION..............................................................................................1 Scope and Motivation................................................................1 Basic Definitions.....................................................................2 GRAPH PARTITIONING PROBLEM............................................................4 Classes of Network Partition....................................................5 Clique Partition Problem.................................................................5 Equipartition Problem...............................................................................5 K-way Equipartition Problem...................................................................5 K-way Partition Problem..........................................................................5 Capacitated Partitioning Problem.............................................................6 Maxcut Problem........................................................................................6 Previous Attempts....................................................................7 Random Solutions.....................................................................................7 Max Flow-Min Cut...................................................................................7 Clustering..................................................................................................8 λ-opting.....................................................................................................9 2-WAY UNIFORM PARTITION...................................................................10 Introduction.........................................................................10 Phase 1 Partition...........................................................................12 Effectiveness of the Procedure..................................................15 Running Time of the Procedure................................................16 Improving Phase 1 Partition...................................................19 Partitioning Unequal Sized Sets...............................................21 Modified Task Performed........................................................22 CONCLUSION.................................................................................................29 REFERENCES..................................................................................................31