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UMass Lowell Computer Science 91.504 Advanced Algorithms Computational Geometry Prof. Karen Daniels Spring, 2001. Lecture 6 Start of Part II Material Monday, 2/4/01. Part 1. Part 2. Course Structure: 2 Parts. Advanced Topics Applications Manufacturing Modeling/Graphics - PowerPoint PPT Presentation
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UMass Lowell Computer Science 91.504 Advanced Algorithms
Computational Geometry Prof. Karen Daniels
Spring, 2001
UMass Lowell Computer Science 91.504 Advanced Algorithms
Computational Geometry Prof. Karen Daniels
Spring, 2001
Lecture 6Lecture 6
Start of Part II MaterialStart of Part II Material
Monday, 2/4/01Monday, 2/4/01
Course Structure: 2 PartsCourse Structure: 2 Parts
Advanced TopicsAdvanced TopicsApplicationsApplications
ManufacturingManufacturingModeling/GraphicsModeling/GraphicsWireless NetworksWireless NetworksVisualizationVisualization
TechniquesTechniques(de)Randomization(de)Randomization
ApproximationApproximationRobustnessRobustness
RepresentationsRepresentationsEpsilon-netEpsilon-netDecomposition treeDecomposition tree
BasicsBasicsPolygon TriangulationPolygon TriangulationPartitioningPartitioning (2D and 3D) Convex (2D and 3D) Convex
HullsHullsVoronoi DiagramsVoronoi DiagramsArrangementsArrangementsSearch/IntersectionSearch/IntersectionMotion PlanningMotion Planning
Syllabus (updated)Syllabus (updated)
Lecture Date Topics Reading HomeworkMon 4/2 Overview of Part II
Project Topics Overviewhandouts &
working groupreport
Assign project proposal
Mon 4/9 Project TopicsCG Libraries Overview
handouts &CG library
documentation
Project proposals due
Tues 4/17 More Depth on Project Topics handouts work on projectMon 4/23 More Depth on Project Topics handouts work on projectMon 4/30 More Depth on Project Topics handouts work on projectMon 5/7 Project Presentations student handouts Project presentations dueMon 5/14 Review Project writeups due
To BeDetermined
Final Exam Cumulative(open book)
Strategic Directions in Computational GeometryStrategic Directions in Computational GeometryWorking Group ReportWorking Group Report
October, 1996October, 1996http://www.cs.brown.edu/people/rt/sdcr/report/report.htmlhttp://www.cs.brown.edu/people/rt/sdcr/report/report.html
Literature for Part II (current plan)Literature for Part II (current plan)
Aspect Milenkovic/Daniels Wu/Li Arya et al. Goodrich/Ramos ShewchuckTitle Translational
PolygonContainmentand MinimalEnclosureusingMathematicalProgramming
Oncalculatingconnecteddominatingset forefficientrouting in adhoc wirelessnetworks
An optimal algorithmfor approximate nearestneighbor searching infixed dimensions
Bounded-IndependenceDerandomizationof GeometricPartitioning withApplications toParallel Fixed-DimensionalLinearProgramming
Triangle: Engineering a 2DQuality Mesh Generator andDelaunay Triangulator
Source Journal: ITOR Conf:Workshop onDiscrete Algand Methodsfor MOBILEComputing&Communications
Journal: ACM Journal: Discrete& Comp Geom
Conf: 1st Workshop on AppliedCG
ApplicationAreas
manufacturing dynamicwirelesscommunications
knowledge discovery;data mining; patternrecognition;classification; machinelearning; datacompression;multimedia databases;document retrieval;statistics
linearprogramming
geometric modeling; graphics
InputObjects
2D nonconvexpolygons
2D pointsrepresentinghosts
d-dimensional points range space PSLG of object
Literature for Part II (current plan)(continued)Literature for Part II (current plan)(continued)
Aspect Milenkovic/Daniels Wu/Li Arya et al. Goodrich/Ramos ShewchuckDimensionality
2D 2D arbitrary arbitrary 2D
Problem/Task
translationalcontainment;overlapelimination;distance-basedsubdivision;minimalenclosure;visibility
dominatingset
partitioning; nearest-neighbor query
geometricrandomization;geometricderandomization
(constrained) Delaunaytriangulation; robustness
Theory?Implementation?
both someexperiments
both theory implementation
ADTs &DataStructures
convex hull;visibilitypolygon
undirectedgraph
balanced box-decomposition tree
epsilon-net;epsilon-approximation
triangular mesh; (constrained)Delaunay triangulation;Voronoi diagram; convex hulls;Guibas/Stolfi quad-edge;triangular data structure; PSLG;splay tree; heap
AlgorithmicParadigms&Techniques
subdivision;approximatealgorithm;binary search
distributed;heuristic
geometricpreprocessing;approximationalgorithm
randomization;derandomization;parallel
sweep-line; geometric divide-and-conquer; incrementalinsertion
Math Topics Minkowskisum; linearprogramming;monotonicity;convexdistancefunction
graph theory:dominatingset
Minkowski metric;probability
VC-dimension;linearprogramming;probability
duality
ProjectProject
ProposalProposal Monday, 4/9Monday, 4/9 2%2%
Interim ReportInterim Report Monday, 4/23Monday, 4/23 5%5%
Final PresentationFinal Presentation Monday, 5/7Monday, 5/7 8%8%
Final SubmissionFinal Submission Monday, 5/14Monday, 5/14 10%10%
25% of course grade25% of course grade
DeliverableDeliverable Due DateDue Date Grade %Grade %
Project Guidelines: ProposalProject Guidelines: Proposal
ObjectiveObjective: State the goal of the project: State the goal of the project PlanPlan: List the tasks you need to accomplish and the date by : List the tasks you need to accomplish and the date by
which you plan to finish themwhich you plan to finish them ResourcesResources: What do you need?: What do you need?
Specialized equipment, language, OS?Specialized equipment, language, OS? Specialized software/libraries?Specialized software/libraries? Additional research papers, books?Additional research papers, books? More background in some area?More background in some area?
Assessment ChecklistAssessment Checklist: Characterize your project : Characterize your project (see next 2 (see next 2 slides)slides)
Guidelines: Proposal (continued)Guidelines: Proposal (continued)
Assessment ChecklistAssessment Checklist::
Characterize your project’s theoretical aspects:Characterize your project’s theoretical aspects:Algorithmic Paradigm DesignAlgorithmic Paradigm DesignAnalysis Technique DesignAnalysis Technique DesignAlgorithm DesignAlgorithm DesignData Structure DesignData Structure DesignAlgorithm and/or Data Structure AnalysisAlgorithm and/or Data Structure Analysis
correctnesscorrectness running time and/or spacerunning time and/or space
Observations/ConjecturesObservations/Conjectures
DifficultyDifficulty
CreativityCreativity
ClarityClarity
OrganizationOrganization
CorrectnessCorrectness
ScopeScope
ImpactImpact
Guidelines: Proposal (continued)Guidelines: Proposal (continued)
Assessment ChecklistAssessment Checklist: : Characterize your project’s implementation aspects:Characterize your project’s implementation aspects:
Reuse of existing Code/LibrariesReuse of existing Code/LibrariesNew CodeNew CodeExperimental DesignExperimental DesignTest SuitesTest SuitesDegenerate/boundary casesDegenerate/boundary casesNumerical robustnessNumerical robustness
CreativityCreativity
ClarityClarity
ImpactImpact
DifficultyDifficulty
OrganizationOrganization
CorrectnessCorrectness
ScopeScope
Guidelines: Final SubmissionGuidelines: Final Submission
AbstractAbstract: Concise overview (at most 1 page): Concise overview (at most 1 page) IntroductionIntroduction: :
Motivation: Why did you choose this project?Motivation: Why did you choose this project? Related Work: Context with respect to CG literatureRelated Work: Context with respect to CG literature Summary of ResultsSummary of Results
Main Body of Paper: (one or more sections)Main Body of Paper: (one or more sections) ConclusionConclusion::
Summary: What did you accomplish?Summary: What did you accomplish? Future Work: What would you do if you had more time?Future Work: What would you do if you had more time?
ReferencesReferences: : Bibliography (papers, books that you used)Bibliography (papers, books that you used)
Well- written final submissions with research content may be Well- written final submissions with research content may be eligible for publishing as UMass Lowell CS technical reports. eligible for publishing as UMass Lowell CS technical reports.
Guidelines: Final SubmissionGuidelines: Final Submission
Main Body of Paper: Main Body of Paper: If your project involves Theory/ Algorithm:If your project involves Theory/ Algorithm:
Informal algorithm description (& example)Informal algorithm description (& example) PseudocodePseudocode Analysis:Analysis:
CorrectnessCorrectness Solutions generated by algorithm are correctSolutions generated by algorithm are correct account for account for
degenerate/boundary/special casesdegenerate/boundary/special cases If a correct solution exists, algorithm finds itIf a correct solution exists, algorithm finds it Control structures (loops, recursions,...) terminate correctly Control structures (loops, recursions,...) terminate correctly
Asymptotic Running Time and/or Space UsageAsymptotic Running Time and/or Space Usage
Guidelines: Final SubmissionGuidelines: Final Submission
Main Body of Paper:Main Body of Paper: If your project involves Implementation:If your project involves Implementation:
Informal descriptionInformal description Resources & Environment: Resources & Environment:
what language did you code in?what language did you code in? what existing code did you use? (software libraries, etc.)what existing code did you use? (software libraries, etc.) what equipment did you use? (machine, OS, compiler)what equipment did you use? (machine, OS, compiler)
AssumptionsAssumptions parameter valuesparameter values
Test casesTest cases tables, figurestables, figures representative examplesrepresentative examples
Guidelines: Interim ReportGuidelines: Interim Report
Structured like Final Submission, except: Structured like Final Submission, except: no Abstract or Conclusionno Abstract or Conclusion fill in only what you’ve done so farfill in only what you’ve done so far can be revised latercan be revised later include a revised proposal if neededinclude a revised proposal if needed identify any issues you have encountered and identify any issues you have encountered and
your plan for resolving them your plan for resolving them
Guidelines: PresentationGuidelines: Presentation
1/2 hour class presentation1/2 hour class presentation Explain to the class what you didExplain to the class what you did Structure it any way you like! Structure it any way you like! Some ideas: Some ideas:
slides slides (electronic or transparency)(electronic or transparency)
demodemo handouts handouts
Project Topics (some possibilities)Project Topics (some possibilities)
Build on a Part I assignment, such as random Build on a Part I assignment, such as random point assignments in 2D or 3Dpoint assignments in 2D or 3D
Navigate Navigate based on line arrangement to do based on line arrangement to do combinatorially-based overlap increase or combinatorially-based overlap increase or reductionreduction
Visualization: Can geometric duality help with Visualization: Can geometric duality help with parallel coordinate representation of high-parallel coordinate representation of high-dimensional data?dimensional data?
)( BA
Project Topics (some possibilities)Project Topics (some possibilities)
Dynamic Wireless Channel Assignment:Dynamic Wireless Channel Assignment: design a heuristic that, given an assignment of design a heuristic that, given an assignment of
frequencies to regions, transforms it into another frequencies to regions, transforms it into another assignment that:assignment that: satisfies a given demand level (number of frequencies) for satisfies a given demand level (number of frequencies) for
each regioneach region respects a separation constraintrespects a separation constraint ““minimizes” the number of frequenciesminimizes” the number of frequencies ‘‘minimizes” the number of frequency reassignmentsminimizes” the number of frequency reassignments