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