Edelsbrunner, H. (1980): Dynamic Rectangle Intersection Searching, Technical University Graz, Institut fur Informationsverarbeitung, Report F 47

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1 279 Edelsbrunner, H. (1980): Dynamic Rectangle Intersection Searching, Technical University Graz, Institut fur Informationsverarbeitung, Report F 47 Edelsbrunner, H. (1982): Intersection Problems in Computational Geometry, Ph. D. thesis, TU Graz Edelsbrunner, H. (1983): An Optimal Solution for Searching in General Planar Subdivisions, TU Graz, Report F 122 Edelsbrunner, H., Maurer, H.A. (1981): A space optimal solution of general region location, TCS 16, Edelsbrunner, H., Maurer, H.A. (1981): On the Intersection of Orthogonal Objects, IPL 13, Edelsbrunner, H., O'Rourke, J., Seidel, R. (1983): Constructing Arrangements of Lines and Hyperplanes with Applications, 24th FOCS, Edelsbrunner, H., Welzl, E. (1983): Halfplanar Range Search in Linear Space and 0(n o. 659 ) Query Time, Technical Report F 111, TU Graz Frederickson, G.n. (1982): Implicit Data Structures for Weighted Elements, Report CS-82-04, Computer Science Department, Penn State University Fredman, M.L. (1981): Lower Bounds on the Complexity of some optimal data structures, SICOMP 10, 1-10 Fredman, M.L. (1981): The Spanning Bound as a Measure of Range Query Complexity, Journal of Algorithms 1, Fredman, M.L. (1981): A lower bound on the complexity of orthogonal range queries, JACM 28, Graham, R.L. (1972): An efficient algorithm for determining the convex hull of a finite planar set, IPL 1, Graham, R.L., Yao, F. (1981): Finding the Convex Hull of a simple polygon, Stanford University, Technical Report CS Green, P.J. (1983): Convex Decomposition of Simple Polygons, typescript

2 280 Guibas, L.J., Yao, F.F. (1980): On Translating a Set of Rectangles, 12th STOC, Gtiting, R.H. (1982): An Optimal Contour Algorithm for Iso-Oriented Rectangles, McMaster University, Report 82-CS-06 Gtiting, R.H. (1983): Conquering Contours: Efficient Algorithms for Computational Geometry, Ph.D. Thesis, CS, Univ. Dortmund Harel, D. (1980): A Linear Time Algorithm for the Lowest Common Ancestor Problem, 21 FOCS, Hertel, St., Mehlhorn, K. (1983): Fast Triangulation of Simple Polygons, FCT, LNCS 158, Hertel, St., Mehlhorn, K., Mantyla, M., Nievergelt, I. (1983): Space Sweep Solves Intersection of Two Convex Polyhedra Elegantly, ACTA INFORMATICA, to appear Kirkpatrick, D.G. (1979): Efficient Computation of Continous Skeletons, 20th FOCS, Kirkpatrick, D.G. (1983): Optimal Search in Planar Subdivisions, SICOMP 12, Kirkpatrick, D.G., Seidel, R. (1982): The ultimate planar convex hull algorithm?, 20th Allerton Conference Ladner, R., (1975): On the structure of polynomial time reducibility, JACM 22, Ladner, R., Lynch, N., Selman, A.L. (1974): Comparison of Polynomial Time Reducibilities, 6th STOC, Lee, D.T., Preparata, F.P. (1977): Location of a Point in a Planar Subdivision and its Applications, SICOMP 6, Lee, D.T., Preparata, F.P. (1979): An optimal algorithm for finding the kernel of a polygon, JACM 25, Lee, D.T., Wong, C.K. (1977): Worst Case Analysis of Region and Partial Region Searches in Multidi mensional Binary Search Trees and Balanced Quad Trees, ACTA INFORMATICA 9, 23-29

3 281 Lueker, G.S. (1978): A Data Structure for Orthogonal Range Queries, 19th FOCS, McCallum, D., Avis, D. (1979): A linear algorithm for finding the convex hull of a simple polygon, IPL 9, McCreight, E.M. (1980): Efficient Algorithms for Enumerating Intersecting Intervals and Rectangles, Xerox Parc Report CSL McCreight, E.M. (1981): Priority Search Trees, Xerox Parc Report CSL-81-5 Mehlhorn, K. (1981): Lower Bounds on the Efficiency of Transforming Static Data Structures into Dynamic Data Structures, Math. Systems Theory 15, 1-11 Mehlhorn, K., Overmars, M.H. (1981): Optimal Dynamization of Decomposable Searching Problems, IPL 12, Monier, L. (1980): Combinatorial solutions of multidimensional divideand-conquer recurrences, J. of Algorithms 1, Muller, D.E., Preparata, F.P. (1978): Finding the Intersection of two convex polyhedra, TCS 7, Nievergelt, I., Preparata, F.P. (1982): Plane-Sweep Algorithms for Intersecting Geometric Figures, CACM, 25, Ottrnann, Th., Widrneyer, P. (1982): On the Placement of Line Segments into a Skeleton Structure, Inst. f. Angewandte Mathematik und Formale Beschreibungsverfahren, D-7500 Karlsruhe, Report No. 117 Ottmann, Th., Widmeyer, P., Wood, D. (1982): A Fast Algorithm for Boolean Mask Operations, Inst. f. Angewandte Mathematik und Formale Beschreibungsverfahren, D-7500 Karlsruhe, Report No. 112 Ottmann, Th., Widmeyer, P., Wood, D. (1982): A Worst-Case Efficient Algorithm for Hidden Line Elimination, Inst. f. Angewandte Mathematik und Formale Beschreibungsverfahren, D-7500 Karlsruhe, Rep. No. 119 Overmars, M.H. (1981): Dynamization of order decomposable set problems, Journal of Algorithms 2,

4 282 Overmars, M.H., van Leeuwen, J. (1981): Maintainance of Configurations in the Plane, JCSS 23, Overmars, M.H., van Leeuwen, J. (1981): Two general methods for dynamization decomposable searching problems, Computing 26, Overmars, M.H., van Leeuwen, J. (1981): worst Case Optimal Insertion and Deletion Methods for Decomposable Searching Problems, IPL 12, Overmars, M.H., van Leeuwen, J. (1982): Dynamic Multi-dimensionsal Data Structures Based on Quad- and k-d Trees, ACTA INFORMATICA 17, Preparata, F.P. (1979): An optimal real time algorithm for planar convex hulls, CACM 22, Prepar.ata, F.P., Hong, S.J. (1977): Convex hulls of finite sets of points in two and three dimensions, CACM 20, Schmidt, A. (1981): Time and Space Bounds for Hidden Line and Hidden Surface Algorithms, Proc. of Eurographics, North Holland Shamos, M.I. (1975): Geometric Complexity, 7th STOC, Sharnos, H.I., Hoey, D Shamos, 11.I., Hoey, D. FOCS, (1975): Closest-Point Problems, 16th FOCS, (1976): Geometric Intersection Problems, 17th Willard, D.E. (1978): New data structures for orthogonal range queries, Technical Report, Harward University Willard, D.E. (1982): Polygon Retrieval, SICOMP 11, Yao, A.C.-C. (1982): Space-Time Trade-off for Answering Range Queries, 14th S 'IDC,

5 283 Subject Index amortized cost 49, 195, 221 binary search 82 - polygon retrieval 66 - range queries 69 - spanning bound 60 convex hull - definition 8J - dynamic 98, 99 - lower bound 98 - order decomposable 81 - point set 98 - simple polygon 93 decomposable searching problem - dynamization 4 - monotone order- 19 dynamization - decomposable 3 lower bounds 9 - order decomposable 19 - weighting 15 duality 246 hidden line elimination 227, 265 intersection - convex polygons 89 - convex polyhedra 173 halfspaces line segments 149, 230 polygons 155, 170 rectangles 198, 210 set of lines 249 inversion 254 least cost paths 264 lower bounds - partial match retrieval 56 measure problem - rectangles 215, polygons 241 multi-dimensional searching - closest point 48 - divide-and-conquer 48 - partial match 25, 29, 43, 56 polygon queries 25, 39, 66 - range queries 25, 36, 69, 185 partial match 25, 29, 43, 56 path decomposition - plane sweep searching subdivisions zig-zag- 264 planar subdivisions - dynamic generalized induced by lines searchingdynamic 135 independent sets 116 other methods 261 path decompositions simple 114 plane sweep - basics intersecting line segments iso-oriented objects triangulation 160 polygon tree 40 polygons - convex polygons hierarchical representation 84

6 284 intersection 92 kernel 259 separation 88 - decomposition intersection 155, triangulation 160 priority search tree 199 range queries 25, 36, 69, 185 range tree 43 recursion equation 50 search - binary search multidimensional- 25 segment tree 212 space sweep 173 spanning trees priority search- J99 - range segment- 212 Voronoi diagram - applications construction 103, insertions, deletions merging 260 transforms - duality inversion 254 traveling salesman 145 trees - d-dimensional interval polygon- 40

7 Springer-Verlag Berlin Heidelberg New York Tokyo QUADPACK A Subroutine Package for Automatic Integration By R.Piessens, E.de Doncker-Kapenga, C. W. Uberhuber, D.K. Kahaner figures. VIII, 301 pages. (Springer Series in Computational Mathematics, Volume 1). ISBN Contents: Introduction Theoretical Background: Automatic Integration with QUADPACK. - Integration Methods. Algorithm Descriptions: QUADPACK contents. - Prototype of Algorithm Description. - Algorithm Schemes. - Heuristics Used in the Algorithms. Guidelines for the Use of QUADPACK: General Remarks. - Decision Tree for Finite-range Integration. - Decision Tree for Infinite-range Integration. - Numerical Examples. - Sample Programs Illustrating the Use of the QUADPACK Integrators. Special Applications of QUADPACK: Two-dimensional Integration. - Hankel Transform. - Numerical Inversion of the Laplace Transform. Implementation Notes and Routine Listings: Implementation Notes. - Routine Listings. References. QUADPACK presents a program package for automatic integration covering a wide variety of problems and various degrees of difficulty. After a theoretical explanation of the quadrature methods, the algorithms used by the integrators are described, providing a detailed outline of the automatic integration strategies. The results for a set of parameter studies reveal efficiency and adequacy for wide ranges of problems. Applications are discussed for solving more complex problems, including double integration, computation of the Hankel transform, and inversion of the Laplace transform. Apart from the explanation of the theory, the book includes the routine listings, the user's manual, and many detailed numerical examples and sample programs. The documentation for use of the package is readable and clear for novice users. With the presentation of the mathematical methods and algorithms, however, some background in the area is assumed.

8 Solving Elliptic Problems Using ELLPACK By J.Rice, R.F.Boisvert Approx. 53 figures. Approx 350 pages. (Springer Series in Computational Mathematics, Volume 2) ISBN Contents: The ELLPACK System: Introduction. - The ELLPACK Language. - Examples. - Advanced Language Facilities. - Extending ELLPACK to Non Standard Problems. The ELLPACK Modules: The ELLPACK Problem Solving Modules. - ITPACK Solution Modules. - The Perfonnance of ELL PACK Software: Performance and its Evaluation. - The Model Problems. - Performance of Modules to Discretize Elliptic Problems. - Performance of Modules to Solve the Algebraic Equations. - Contributor's Guide: Software Parts for Elliptic Problems. - Interface Specifications. - Module Interface Access. - Programming Standards. - Preprocessor Data. - System Programmer's Guide: Installing the ELLPACK System. - Tailoring the ELLPACK System. - Appendices: The PDE Population. - The PG System. - The Template Processor. Springer-Verlag Berlin Heidelberg New York Tokyo This book is a complete guide to the ELLPACK software system solving elliptic partial differential equations. ELLPACK consists of a very high level user interface to over 50 problem solving moldules. These modules are state of the art software for two and three dimensional problems and include [mite difference, fmite element, SFT, multigrid and many other capabilities. The book gives the practicing scientists the tools to solve a wide range of elliptic problems with minimum effort. It shows system programmers how to install and modify ELLPACK and experts how to adapt ELLPACK to a wide range of applications.