1. UMass Lowell Computer Science 91.504 Advanced Algorithms Computational Geometry Prof. Karen Daniels Spring, 2004 Lecture 1 Course Introduction

2. What is Computational Geometry?

3. Advanced Algorithms Computational Geometry Telecommunications Visualization 91.504 Manufacturing ComputerGraphics Design Analyze Apply CAD

4. Sample Application Areas Computer Graphics Geographic Information Systems Robotics Bioinformatics Astrophysics MedicalImaging Telecommunications Data Mining & Visualization

5. Typical Problems ä bin packing ä Voronoi diagram ä simplifying polygons ä shape similarity ä convex hull ä maintaining line arrangements ä polygon partitioning ä nearest neighbor search ä kd-trees SOURCE: Steve Skiena’s Algorithm Design Manual (for problem descriptions, see graphics gallery at ) (for problem descriptions, see graphics gallery at http://www.cs.sunysb.edu/~algorith)

6. Common Computational Geometry Structures Voronoi Diagram Convex Hull New Point source: O’Rourke, Computational Geometry in C Delaunay Triangulation

7. Sample Tools of the Trade Algorithm Design Patterns/Techniques: binary searchdivide-and-conquerduality randomizationsweep-line derandomizationparallelism Algorithm Analysis Techniques: asymptotic analysis, amortized analysis Data Structures: winged-edge, quad-edge, range tree, kd-tree Theoretical Computer Science principles: NP-completeness, hardness Growth of Functions Summations Recurrences Sets Probability MATH Proofs Geometry Graph Theory Combinatorics Linear Algebra

8. Computational Geometry in Context TheoreticalComputerScience Applied Computer Science AppliedMath Geometry ComputationalGeometryEfficient Geometric Algorithms Design Analyze Apply

9. Course Introduction Course Description

10. Web Page http://www.cs.uml.edu/~kdaniels/courses/ALG_504.html

11. Nature of the Course ä Elective graduate Computer Science course ä Theory and Practice ä Theory: “Pencil-and-paper” exercises ä design an algorithm ä analyze its complexity ä modify an existing algorithm ä prove properties ä Practice ä Programs ä Real-world examples

12. Course Structure: 2 Parts Advanced Topics (may change) (may change)ApplicationsManufacturingModeling/Graphics Wireless Networks VisualizationTechniques(de)RandomizationApproximationRobustnessRepresentations Decomposition trees Basics Polygon Triangulation Partitioning Convex Hulls Voronoi Diagrams ArrangementsSearch/Intersection Motion Planning papers from literature

13. Textbook - - Required: ä Computational Geometry in C ä second edition ä by Joseph O’Rourke ä Cambridge University Press ä 1998 ä see course web site for ISBN number(s) & errata list available on-line Web Site: http://cs.smith.edu/~orourke/books/compgeom.html + conference, journal papers

14. Textbook Java Demo Applet Code functionChapter pointerdirectory ----------------------------------------------------- TriangulateChapter 1, Code 1.14/tri Convex Hull(2D)Chapter 3, Code 3.8/graham Convex Hull(3D)Chapter 4, Code 4.8/chull sphere.cChapter 4, Fig. 4.15/sphere Delaunay Triang Chapter 5, Code 5.2/dt SegSegIntChapter 7, Code 7.2/segseg Point-in-polyChapter 7, Code 7.13/inpoly Point-in-hedronChapter 7, Code 7.15/inhedron Int Conv PolyChapter 7, Code 7.17/convconv Mink ConvolveChapter 8, Code 8.5/mink Arm Move Chapter 8, Code 8.7/arm http://cs.smith.edu/~orourke/books/CompGeom/CompGeom.html

15. Prerequisites ä Graduate Algorithms (91.503) ä Coding experience in C, C++ or Java ä Standard CS graduate-level math prerequisites + high school Euclidean geometry ä additional helpful math background: ä linear algebra, topology Growth of Functions Summations Recurrences Sets Probability MATH Proofs Geometry

16. Syllabus (current plan) DateTopicsReadingHomework Part I: Fundamentals Wed 1/28Introduction Overview of Part I Review Cormen et al. Ch 33 LEDA Introduction/Triangulation Polygon Triangulation Cormen et al. Ch 33 LEDA documentation O’Rourke: Ch1 assign #1 (O’Rourke: Ch1, LEDA exercise) Wed 2/4Polygon Triangulation Polygon Partitioning LEDA Polygon Partitioning O’Rourke: Ch1 O’Rourke: Ch2 LEDA documentation Wed 2/112D Convex Hulls 3D Convex Hulls LEDA Convex Hulls O’Rourke: Ch3 O’Rourke: Ch4 LEDA documentation #1 due assign #2 (Ch2,3) Wed 2/18Voronoi Diagrams LEDA Voronoi Diagrams LEDA Delaunay Diagrams O’Rourke: Ch5 LEDA documentation #2 due assign #3 (Ch4,5) Wed 2/25Arrangements Search & Intersection LEDA Intersection O’Rourke: Ch6 O’Rourke: Ch7 LEDA documentation #3 due assign #4 (Ch6,7) Wed 3/3Motion Planning LEDA Minkowski Sum Review O’Rourke O’Rourke: Ch8 LEDA documentation O’Rourke Ch1-8 #4 due assign #5 (Ch8) Wed 3/10Midterm ExamO’Rourke Ch1-8#5 due

17. Syllabus (current plan) DateTopicsReadingHomework Part II: Advanced Topics Wed 3/24Overview of Part II Project Topics Overview -Advanced Techniques - Advanced Applications handouts project proposal assigned Wed 3/31Project Topics Overview - Advanced Techniques -Advanced Applications handoutspreliminary topic choice Wed 4/7Students lead class discussion on readings related to their projects handoutsproject proposals due Wed 4/14More depth on project topicshandouts project status report & background/related work section due Wed 4/28More depth on project topicshandoutsproject status report & algorithm design section due Wed 5/5More depth on project topicshandoutsproject status report & implementation section due Wed 5/12Project Presentationsproject presentations, writeups due

18. Important Dates ä Midterm Exam:Wednesday, 3/10 ä Final Exam:none If you have conflicts with exam date, please notify me as soon as possible.

19. Grading ä ä Homework35% ä ä Project35% ä ä Midterm (O’Rourke) 30% (open book, notes ) * *Some project writeups may be eligible for submission to the annual Canadian Conference on Computational Geometry, to be held in Montreal from 9-11 August, 2004.

20. Course Introduction My Computational Geometry Research

21. My Previous Applied Algorithms Research ä VLSI Design: ä Custom layout algorithms for silicon compiler ä Geometric Modeling: ä Partitioning cubic B- spline curves ä Manufacturing: ä see taxonomy on next slide

22. Taxonomy of Problems Supporting Apparel Manufacturing OrderedContainment Geometric Restriction Distance-BasedSubdivision MaximumRectangle Limited Gaps MinimalEnclosure Column-Based Layout Two-Phase Layout LatticePacking Containment Maximal Cover

23. My Applied Algorithms Research Focus at UMass Lowell Telecommunications Data Mining, Visualization,Bioinformatics Manufacturing Design Analyze Apply for covering, assignment, clustering, packing, layout feasibility, optimization problems CAD

24. New Research in Translational 2D Covering [CCCG 2001,03] Q3Q3 Q1Q1 Q2Q2 Sample P and Q P1P1 P2P2 Translated Q Covers P P1P1 Q1Q1 Q2Q2 Q3Q3 P2P2 Translational 2D Polygon Covering ä Input: ä Covering polygons Q = {Q 1, Q 2,..., Q m } ä Target polygons (or point-sets) P = {P 1, P 2,..., P n } ä Output:  Translations  = {  1,  2,...,  m } such that Joint work with graduate student R. Inkulu, A. Mathur and UNH Prof. Roger Grinde

25. New Research in Dynamic Channel Assignment [GLOBECOM 2001, INFORMS Telecom 2004] ä Input: ä Number of time periods ä 7 x 7 square cell grid ä Set of channels ä Co-channel interference threshold B = 27234 ä Demand for each time period ä Output: ä For each time period ä Feasible assignment of channels to cells satisfying: ä Demand model ä Co-channel interference constraints ä (SignalStrength/Interference) > B ä Computation time limit ä Minimize number of channels used ä Minimize reassignments across time solution assumes no channel repetition within any 2 x 2 square Sample solution for 1 time period Demand Assignment 5 different channels are used Joint work with Prof. Chandra, graduate students S. Liu, S.Widhani, H. Rathi

26. Manufacturing Inventory Optimization ä Using Ordinal Optimization [Ho, Harvard] to schedule factory production Joint work with: PhD student S. Bouhia in Harvard’s Division of Engineering & Applied Sciences and Center for Textile & Apparel Research; also UMass Lowell graduate students S. Gupta & S. Banker

27. New Research in Bioinformatics ä Proposed Hemoglobin Assembly Simulation: ä Model molecular environment ä Can a molecular complex “fit” into environment? ä 3D containment ä Joint proposed work with Prof. McDonald Figure: from NSF proposal Figure: clustering results from Harel, Koren ä Clustering: ä Graduate student Sei-Hyung Lee

28. New Geometric Research Sponsored by NSF/DARPA ä Spline Covering Joint work with graduate student C. Neacsu and Profs. Klain, Rybnikov ä Estimating Topological Properties

29. Sample of Supporting Algorithmic & Math Areas & Techniques ä Computational Geometry ä Convex hulls ä Visibility polygons ä Arrangements ä Mathematical Programming ä Linear programming ä Integer programming ä Lagrangian relaxation ä Upper, lower bounding ä Dynamic Data Structures ä Algorithm Design Patterns ä search space subdivision ä binary search ä divide-and-conquer ä sweep-line ä discrete-event simulation ä Algorithm Analysis Techniques ä Complexity Theory ä NP-completeness, hardness ä Discrete Math ä Minkowski sum ä Monotone matrices ä Lattices ä Set operations: union, intersection, difference

30. ISET Research Scholars Program Information Sciences, Engineering and Technology ä Research projects ä Technical leadership ä Faculty mentors ä Scholarship support ä Sponsors ä National Science Foundation ä UMass Lowell ä Lucent Technologies ä Selected Current Research Project Areas ä Telecommunications ä Wireless Networks ä Network Performance ä Systems ä Multimedia Systems ä Acoustics ä Computer Science ä Network Security ä Complexity Theory ä Robotics For additional details and application information: http://morse.uml.edu/iset.html applicant screening is underway for Spring, 2004

31. Key Partners & Resources Design Analyze Apply for covering, assignment, clustering, packing, layout feasibility, optimization problems Students: PhD, MS, undergrad AppliedAlgorithmsLab: OS 307 Computers:SparcUltras,PCs Software Libraries: CPLEX, CGAL, LEDA Affiliations:CACT IVPR IVPRHCTAR Algorithms Courses & Research Seminar: 91.503, 91.504, 91.404

32. Machine Accounts ä Each student will have an account on my machine: minkowski.cs.uml.edu. ä Username will be the same as your username on CS. ä Password will be your initials followed by the last 5 digits on the bottom right hand corner of the back of your student id card. ä To remotely log in, use a secure shell (e.g. ssh). ä To transfer files, use a secure FTP (e.g. sftp). ä LEDA and CGAL libraries are on minkowski.