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Applied Algorithms Research Assoc. Prof. Karen Daniels

Core Geometric &. Combinatorial Algorithms. Applied Algorithms Research Assoc. Prof. Karen Daniels. Channel Assignment for Telecommunications. Design. Analyze. Covering for Geometric Modeling. feasibility, estimation, optimization problems. for

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Applied Algorithms Research Assoc. Prof. Karen Daniels

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  1. Core Geometric & Combinatorial Algorithms Applied Algorithms ResearchAssoc. Prof. Karen Daniels Channel Assignment for Telecommunications Design Analyze Covering for Geometric Modeling feasibility, estimation, optimization problems for covering, assignment, clustering, packing, layout, geometric modeling Data Mining, Clustering, for Bioinformatics Application-Based Algorithms Apply Topological Invariant Estimation for Geometric Modeling Meshing for Geometric Modeling Packing for Manufacturing Courtesy of Cadence Design Systems

  2. Translational 2D Polygon Covering P2 P2 P1 Q3 P1 Q2 Q2 Q1 Sample P and Q Translated Q Covers P Q1 Q3 Covering: 2D Polygonal Covering [CCCG 2001,CCCG2003] Supported under NSF/DARPA CARGO program • Input: • Covering polygons Q = {Q1, Q2 , ... , Qm} • Target polygons (or point-sets) P = {P1, P2 , ... , Pn} • Output: • Translations g = {g1, g2 , ... , gm} such that With graduate students R. Inkulu, A. Mathur, C.Neacsu, & UNH professor R. Grinde

  3. Covering: 2D B-Spline Covering [CORS/INFORMS2004, UMass Lowell Student Research Symposium 2004, Computers Graphics Forum, 2006] Supported under NSF/DARPA CARGO program With graduate student C. Neacsu

  4. Covering: Box Covering[12th WSEAS Int. Conf. on Computers, 2008] Supported under NSF/DARPA CARGO program • Goal: Translate boxes to cover another box • Orthotope (box) covering in 2D, 3D, … 2D views of 3D covering Full cover Partial cover (red part uncovered) With Masters student B. England

  5. Covering: Covering Web Sitehttp://www.cs.uml.edu/~kdaniels/covering/covering.htm With graduate student C. Neacsu and undergraduate A. Hussin

  6. Geometric Modeling: Estimating Topological Properties from a Point Sample[4th Int. Symp. on 3D Data Processing, Visualization and Transmission, 2008] Supported under NSF/DARPA CARGO program • Euler characteristic: c = #(components) - #(tunnels) + #(bubbles) Heart MRI data Stanford bunny Cube with 3 crossing tunnels: c = -4 With graduate student C. Neacsu, UMass Amherst student B. Jones, UML Math Profs. Klain, Rybnikov, students N. Laflin, V. Durante

  7. Geometric Modeling: Mesh Generation for Finite Element Modeling [accepted as Research Note for 17th Int. Meshing Roundtable, 2008, and Fall CG Workshop, 2009] • Needed for signal integrity in printed circuit board interconnect routing • 2D constrained Delaunay triangulation is extruded into 3D to form triangular prism mesh Courtesy of Cadence Design Systems Doctoral student S. Ye

  8. Computational Geometry: Thrackle Extensibility [CCCG 2006] • Thrackle: • Drawing of a simple graph on the plane: • each edge drawn as a smooth arc with distinct end-points, • every two edges have exactly one common point, • endpoints of each edge are two vertices; • no edge crosses itself. • Conway’s thrackle conjecture: • Number of edges for n vertices is at most n. With graduate student W. Li and Math Prof. Rybnikov

  9. Bioinformatics: Improved Support Vector Clustering[ICBA2004, SIAM Data Mining 2006, UMass Lowell Student Research Symposium 2003 ] • Goal: Find natural groupings of data points • Support Vector Clustering based on machine learning method With doctoral student S. Lee

  10. ISET Research Scholars Program Information Sciences, Engineering and Technology Faculty mentors Scholarship support Sponsored by National Science Foundation Research Projects • Optimizing Channel Allocation in Wireless Networks • H. Rathi (2002-2003) • Modeling Hemoglobin Formation • S. Kundu (2003) • S. Rathi (2003) • Flow Networks • S. Casey (2005) Research Projects • Polygonal Covering • S. MacFarland (2005) • A. Hussin (2005) • Algorithm Efficiency • A. Singh (2006) • Random Forests for Cancer Classification • L. Liang (2006) • Bioinformatics • N. Laflin (2006) • Topological Estimation • N. Laflin, V. Durante (2006) This program was funded by NSF from Fall, 2001 - Summer, 2007.

  11. Design Analyze feasibility, optimization problems Core Geometric & for covering, assignment, clustering, packing, layout Combinatorial Algorithms Application-Based Algorithms Apply Key Partners & Resources Affiliations: CACT IVPR HCTAR Students: ScD, MS, undergrad Computers: SparcUltras, Sun Blades, PCs Algorithms & Geometry Related Courses: 91.503, 91.504, 91.404, 91.580 Applied Algorithms Lab: OS 220B Software Libraries: CPLEX, CGAL, LEDA

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