1. 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

2. Course Structure: 2 Parts Advanced Topics ApplicationsManufacturingModeling/Graphics Wireless Networks VisualizationTechniques(de)RandomizationApproximationRobustnessRepresentationsEpsilon-net Decomposition tree Basics Polygon Triangulation Partitioning (2D and 3D) Convex Hulls (2D and 3D) Convex Hulls Voronoi Diagrams ArrangementsSearch/Intersection Motion Planning

3. Syllabus (updated) Strategic Directions in Computational Geometry Working Group Report October, 1996 http://www.cs.brown.edu/people/rt/sdcr/report/report.html

4. Literature for Part II (current plan)

5. Literature for Part II (current plan) (continued)

6. Project ProposalMonday, 4/92% Interim ReportMonday, 4/235% Final PresentationMonday, 5/78% Final SubmissionMonday, 5/1410% 25% of course grade DeliverableDue Date Grade %

7. Project Guidelines: Proposal ä Objective: State the goal of the project ä Plan: List the tasks you need to accomplish and the date by which you plan to finish them ä Resources: What do you need? ä Specialized equipment, language, OS? ä Specialized software/libraries? ä Additional research papers, books? ä More background in some area? ä Assessment Checklist: Characterize your project (see next 2 slides)

8. Guidelines: Proposal (continued) ä Assessment Checklist: ä Characterize your project’s theoretical aspects: ä Algorithmic Paradigm Design ä Analysis Technique Design ä Algorithm Design ä Data Structure Design ä Algorithm and/or Data Structure Analysis ä correctness ä running time and/or space ä Observations/Conjectures Difficulty Creativity Clarity Organization Correctness Scope Impact

9. Guidelines: Proposal (continued) ä Assessment Checklist: ä Characterize your project’s implementation aspects: ä Reuse of existing Code/Libraries ä New Code ä Experimental Design ä Test Suites ä Degenerate/boundary cases ä Numerical robustness Creativity Clarity Impact Difficulty Organization Correctness Scope

10. Guidelines: Final Submission ä Abstract: Concise overview (at most 1 page) ä Introduction: ä Motivation: Why did you choose this project? ä Related Work: Context with respect to CG literature ä Summary of Results ä Main Body of Paper: (one or more sections) ä Conclusion: ä Summary: What did you accomplish? ä Future Work: What would you do if you had more time? ä References: Bibliography (papers, books that you used) Well- written final submissions with research content may be eligible for publishing as UMass Lowell CS technical reports.

11. Guidelines: Final Submission ä Main Body of Paper: ä If your project involves Theory/ Algorithm: ä Informal algorithm description (& example) ä Pseudocode ä Analysis: ä Correctness ä Solutions generated by algorithm are correct ä account for degenerate/boundary/special cases ä If a correct solution exists, algorithm finds it ä Control structures (loops, recursions,...) terminate correctly ä Asymptotic Running Time and/or Space Usage

12. Guidelines: Final Submission ä Main Body of Paper: ä If your project involves Implementation: ä Informal description ä Resources & Environment: ä what language did you code in? ä what existing code did you use? (software libraries, etc.) ä what equipment did you use? (machine, OS, compiler) ä Assumptions ä parameter values ä Test cases ä tables, figures ä representative examples

13. Guidelines: Interim Report ä Structured like Final Submission, except: ä no Abstract or Conclusion ä fill in only what you’ve done so far ä can be revised later ä include a revised proposal if needed ä identify any issues you have encountered and your plan for resolving them

14. Guidelines: Presentation ä 1/2 hour class presentation ä Explain to the class what you did ä Structure it any way you like! ä Some ideas: ä slides (electronic or transparency) ä demo ä handouts

15. Project Topics (some possibilities) ä Build on a Part I assignment, such as random point assignments in 2D or 3D ä Navigate based on line arrangement to do combinatorially-based overlap increase or reduction ä Visualization: Can geometric duality help with parallel coordinate representation of high- dimensional data?

16. Project Topics (some possibilities) ä Dynamic Wireless Channel Assignment: ä design a heuristic that, given an assignment of frequencies to regions, transforms it into another assignment that: ä satisfies a given demand level (number of frequencies) for each region ä respects a separation constraint ä “minimizes” the number of frequencies ä ‘minimizes” the number of frequency reassignments