Containment Algorithms for Nonconvex Polygons with Applications to Layout The Harvard community has made this article openly available. Please share how this access benefits you. Your story matters Citation McIntosh Daniels, Karen. 1995. Containment Algorithms for Nonconvex Polygons with Applications to Layout. Harvard Computer Science Group Technical Report TR-12-95. Citable link http://nrs.harvard.edu/urn-3:HUL.InstRepos:34310069 Terms of Use This article was downloaded from Harvard University’s DASH repository, and is made available under the terms and conditions applicable to Other Posted Material, as set forth at http:// nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of- use#LAA Containment Algorithms for Nonconvex Polygons with Applications to Layout Karen McIntosh Daniels TR May Center for Research in Computing Technology Harvard University Cambridge Massachusetts Containment Algorithms for Nonconvex Polygons with Applications to Layout A thesis presented by Karen McIntosh Daniels to The Division of Applied Sciences in partial fulllment of the requirement for the degree of Do ctor of Philosophy in the sub ject of Computer Science Harvard University Cambridge Massachusetts May c by Karen McIntosh Daniels All rights reserved Table of Contents List of Figures List of Tables Introduction Background Containment Packing and Layout Thesis Statement and Overview of Chapter Overview of Containment Work Related Work Our Containment Work Overview of Layout Work Related Work Convex Items Nonconvex Items Assignment Our Layout Work Pro ject Background Compaction Panel Placement Trim Placement Benchmarks Contribution Overview I Translational Containment Preliminaries Introduction Overview of Chapter Notation Hardness The RestrictEvaluateSubdivid e Paradigm Approach to Running Time Analysis Related Work Containment Characterization Overview of Part One Conguration Space Restrictions Introduction Overview Notation Prop erties of Valid Restrictions Boundary Intersection Lo ose Fits Annular Conguration Spaces Size and sAnalysis Identical Items SteadyState Geometric Restriction Avnaim and Boissonnats Solutions to NN and NP SteadyState Restriction Running Time Example Eectiveness SteadyState Linear Programming Restriction Example Eectiveness Subset Restriction Union Restriction CharacterizationBased Restriction Symmetry Breaking and Subset Substitution Restrictions Closed Op erators Summary and Conclusions Evaluation and Sub division Introduction Evaluation Sub division Overview Greedy Evaluation Algorithm Heuristics for Selecting u ij Comparing Heuristics for Selecting u ij Overlap Reduction Evaluation Evaluation of a Restricted U Sub division Denition and Goals SizeBased Metho d CombinatoriallyBased Metho ds DistanceBased Metho d Summary and Conclusions Algorithms Introduction Overview An Approximate Containment Algorithm Introduction Analysis Results A Hybrid Containment Algorithm Introduction Results Conclusion Summary and Conclusions II Applications of Containment to Layout Preliminaries Introduction Overview of Chapter Overview of Container Transformation Work Overview of Minimal Container Work Related Work Our Minimal Container Work Overview of Maximal Item Work Our Maximal Item Work Overview of Part Two Limited Gaps Introduction Decomp osing the Container into Gaps Overview The Challenge of Constructing Gap Sets Compaction Partitioning Squares Other Metho ds Limited Gaps Reachable Regions Dening Limited Gaps using Probability of Interference Ecient Computation of Limited Gaps Breaking Polygons Inking Polygons MAAPRs Summary of MAAPR Results .