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

With graduate students R. Inkulu, A. Mathur, C.Neacsu, & UNH professor R. Grinde Covering: 2D Polygonal Covering [CCCG 2001,CCCG2003] 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 Supported under NSF/DARPA CARGO program

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

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

Covering: Covering Web Site With graduate student C. Neacsu and undergraduate A. Hussin

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

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

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

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

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

Key Partners & Resources Design Analyze Apply for covering, assignment, clustering, packing, layout feasibility, optimization problems Students: ScD, MS, undergrad AppliedAlgorithmsLab: OS 220B Computers:SparcUltras, Sun Blades, PCs Software Libraries: CPLEX, CGAL, LEDA Affiliations:CACT IVPR IVPRHCTAR Algorithms & Geometry Related Courses: , , ,