Dinesh P. Mehta

Handbook of Data Structures and Applications

Fundamentals Analysis of Algorithms Sartaj Sahni University of Florida, Gainesville, USA Basic Structures Dinesh P. Mehta Colorado School of Mines, Golden, Colorado, USA Trees Dinesh P. Mehta Graphs Narsingh Deo University of Central Florida, Orlando, USA Priority Queues Leftist Trees Sartaj Sahni Skew Heaps C. Pandu Rangan Indian Institute of Technology, Madras, Chennai Binomial, Fibonacci, and Pairing Heaps Michael L. Fredman Rutgers University, New Brunswick, New Jersey, USA Double-Ended Priority Queues Sartaj Sahni Dictionary Structures Hash Tables Pat Morin Carleton University, Ottawa, Ontario, Canada Balanced Binary Search Trees Arne Andersson, Uppsala University, Sweden Rolf Fagerberg and Kim S. Larsen, University of Southern Denmark, Odense Finger Search Trees Gerth Stolting Brodal University of Aarhus, Denmark Splay Trees Sanjeev Saxena Indian Institute of Technology, Kanpur Randomized Dictionary Structures C. Pandu Rangan Trees with Minimum Weighted Path Length Wojciech Rytter New Jersey Instituteof Technology, Newark, USA B. Trees Donghui Zhang Northeastern University, Boston, Massachusetts, USA Multidimensional and Spatial Structures Multidimensional Spatial Data Structures Hanan Samet University of Maryland, College Park, USA Planar Straight Line Graphs Siu-Wing Cheng The Hong Kong University of Science and Technology, Kowloon Interval, Segment, Range, and Priority Search Trees D. T. Lee Academia Sinica, Taipei, Taiwan Quadtrees and Octrees Srinivas Aluru Iowa State University, Ames, USA Binary Space Partitioning Trees Bruce F. Naylor University of Texas, Austin, USA R-Trees Scott Leutenegger and Mario A. Lopez University of Denver, Colorado, USA Managing Spatio-Temporal Data Sumeet Dua Louisiana Tech University, Ruston, USA S. S. Iyengar Louisiana State University, Baton Rouge, USA Kinetic Data Structures Leonidas Guibas Stanford University Palo Alto, California, USA Online Dictionary Structures Teofilo F. Gonzalez University of California, Santa Barbara, USA Cuttings Bernard Chazelle Princeton University, Princeton, New Jersey, USA Approximate Geometric Query Structures Christian A. Duncan University of Miami, Florida, USA Michael T. Goodrich University of California, Irvine, USA Geometric and Spatial Data Structures in External Memory Jeffrey Scott Vitter Purdue University West Lafayette, Indiana, USA Miscellaneous Data Structures Tries Sartaj Sahni Suffix Trees and Suffix Arrays Srinivas Aluru String Searching Andrzej Ehrenfeuch University of Colorado, Boulder, USA Ross M. McConnell Colorado State University, Fort Collins, USA Persistent Data Structures Haim Kaplan Tel Aviv University, Israel PC Trees Wen-Lian Hsu Academia Sinica, Taipei, Taiwan Ross M. McConnell Data Structures for Sets Rajeev Raman University of Leicester, UK Cache-Oblivious Data Structures Lars Arge Duke University, Durham, North Carolina, USA, Gerth Stolting Brodal University of Aarhus, Denmark Rolf Fagerberg Dynamic Trees Camil Demetrescu, Irene Finocchi, and Giuseppe F. Italiano Universita di Roma, Italy Dynamic Graphs Camil Demetrescu, Irene Finocchi, and Giuseppe F. Italiano Succinct Representation of Data Structures J. Ian Munro and S. Srinivasa Rao University of Waterloo, Ontario, Canada Randomized Graph Data-Structures for Approximate Shortest Paths Surender Baswana and Sandeep Sen Indian Institute of Technology, Delhi, India Searching and Priority Queues in o(log n) Time Arne Andersson Data Structures in Languages and Libraries Functional Data Structures Chris Okasaki United States Military Academy, West Point, New York LEDA, a Platform for Combinatorial and Geometric Computing Stefan Naeher University of Trier, Germany Data Structures in C++ Mark Allen Weiss Florida International University, Miami, USA Data Structures in JDSL Michael T. Goodrich Roberto Tamassia, and Luca Vismara Brown University, Providence, Rhode Island, USA Data Structure Visualization John Stasko Georgia Institute of Technology, Atlanta, USA Drawing Trees Sebastian Leipert Center of Advanced European Studies and Research, Bonn, Germany Drawing Graphs Peter Eades and Seok-Hee Hong University of Sydney and NICTA, Australia Concurrent Data Structures Mark Moir and Nir Shavit Sun Microsystems Laboratories, Burlington, Massachusetts, USA Applications IP Router Tables Sartaj Sahni Kun Suk Kim and Haibin Lu University of Florida, Gainesville, USA Multi-Dimensional Packet Classification Pankaj Gupta Cypress Semiconductor, San Jose, California, USA Data Structures in Web Information Retrieval Monika Henzinger Google, Inc., Mountain View, California, USA The Web as a Dynamic Graph S.N.Maheshwari Indian Institute of Technology, Madras, Chennai Layout Data Structures Dinesh P. Mehta Floorplan Representation in VLSI Zhou Fen Fudan University, Shanghai, China Bo Yao, and Chung-Kuan Cheng University of California, San Diego Computer Graphics Dale McMullin and Alyn Rockwood Colorado School of Mines, Golden, USA Geographic Information Systems Bernhard Seeger University of Marburg, Germany Peter Widmayer ETH, Zurich, Switzerland Collision Detection Ming C. Lin and Dinesh Manocha University of North Carolina, Chapel Hill, USA Image Data Structures S. Sitharama Iyengar V. K. Vaishnavi Georgia State University, Atlanta, USA S. Gunasekaran Louisiana State University, Baton Rouge, USA Computational Biology Stefan Kurtz University of Hamburg, Germany Stefano Lonardi University of California, Riverside, USA Elimination Structures in Scientific Computing Alex Pothen Old Dominion University, Norfolk, Virginia, USA Sivan Toledo Tel Aviv University, Israel Data Structures for Databases Joachim Hammer and Markus Schneider University of Florida, Gainesville, USA Data Mining Vipin Kumar and Michael Steinbach University of Minnesota, Minneapolis, USA Pang-Ning Tan Michigan State University, East Lansing, USA Computational Geometry: Fundamental Structures Mark de Berg and Bettina Speckmann Technical University, Eindhoven, The Netherlands Computational Geometry: Proximity and Location Sunil Arya The Hong Kong University of Scienceand Technology, Kowloon David M. Mount University of Maryland, College Park, USA Computational Geometry: Generalized Intersection Searching Prosenjit Gupta International Institute of Information Technology, Hyderabad, India Ravi Janardan University of Minnesota, Minneapolis, USA Michiel Smid Carleton University, Ottawa, Ontario, Canada

Handbook of Algorithms for Physical Design Automation

The physical design flow of any project depends upon the size of the design, the technology, the number of designers, the clock frequency, and the time to do the design. As technology advances and design-styles change, physical design flows are constantly reinvented as traditional phases are removed and new ones are added to accommodate changes in technology. Includes a personal perspective from Ralph Otten as he looks back on the major technical milestones in the history of physical design automation. Explore State-of-the-Art Techniques and TrendsHandbook of Algorithms for Physical Design Automation provides a detailed overview of VLSI physical design automation, emphasizing state-of-the-art techniques, trends and improvements that have emerged during the previous decade. After a brief introduction to the modern physical design problem, basic algorithmic techniques, and partitioning, the book discusses significant advances in floorplanning representations and describes recent formulations of the floorplanning problem. The text also addresses issues of placement, net layout and optimization, routing multiple signal nets, manufacturability, physical synthesis, special nets, and designing for specialized technologies. Highly-Focused Information for Next Generation Design Problems Although several books on this topic are currently available, most are either too broad or out of date. Alternatively, proceedings and journal articles are valuable resources for researchers in this area, but the material is widely dispersed in the literature. This handbook pulls together a broad variety of perspectives on the most challenging problems in the field, and focuses on emerging problems and research results.

Optimal coverage paths in ad-hoc sensor networks

This paper discusses the computation of optimal coverage paths in an ad-hoc network consisting of n sensors. Improved algorithms, with a preprocessing time of O(n log n), to compute a maximum breach/support path P in optimal (|P|) time or the maximum breach/support value in O(1) time are presented. Algorithms for computing a shortest path that has maximum breach/support are also provided. Experimental results for breach paths show that the shortest path length is on the average 30% less and is not much worse that the ideal straight line path. For applications that require redundancy (i.e., detection by multiple sensors), a generalization of Voronoi diagrams allows us to compute maximum breach paths where breach is defined as the distance to the kth nearest sensor in the field. Extensive experimental results are provided.

Heterogeneous floorplanning for FPGAs

The large size of modern FPGAs has caused researchers to consider deploying hierarchical techniques in their design. In this paper, we consider the floorplanning of FPGAs. We present a two-step approach for the floorplanning of modern FPGAs that we believe is cleaner and more versatile than recent floorplanners. The steps, based on resource-aware fixed outline simulated annealing and constrained floorplanning, are adapted to address the heterogeneous nature of FPGA floorplanning. Experiments demonstrate the viability of our approach.

Automated reaction mapping

Automated reaction mapping is a fundamental first step in the analysis of chemical reactions and opens the door to the development of sophisticated chemical kinetic tools. This article formulates the reaction mapping problem as an optimization problem. The problem is shown to be NP-Complete for general graphs. Five algorithms based on canonical graph naming and enumerative combinatoric techniques are developed to solve the problem. Unlike previous formulations based on limited configurations or classifications, our algorithms are uniquely capable of mapping any reaction that can be represented as a set of chemical graphs optimally. This is due to the direct use of Graph Isomorphism as the basis for these algorithms as opposed to the more commonly used Maximum Common Subgraph. Experimental results on chemical and biological reaction databases demonstrate the efficiency of our algorithms.

An open-source java platform for automated reaction mapping.

This article presents software applications that have been built upon a modular, open-source, reaction mapping library that can be used in both cheminformatics and bioinformatics research. We first describe the theoretical underpinnings and modular architecture of the core software library. We then describe two applications that have been built upon that core. The first is a generic reaction viewer and mapper, and the second classifies reactions according to rules that can be modified by end users with little or no programming skills.

On the use of flexible, rectilinear blocks to obtain minimum-area floorplans in mixed block and cell designs

This paper presents three minimum-area floorplanning algorithms that use flexible arbitrary rectilinear shapes for the standard cell regions in MBC design. The first algorithm (pure HCST) introduces a grid traversal technique which guarantees a minimum-area floorplan. The second algorithm (Hybrid-BF) uses a combination of HCST and Breadth First (BF) traversals to give a practical solution that approximately places flexible blocks at specified locations called seeds. The third algorithm (Hybrid-MBF) improves on the shapes of the flexible blocks generated by Hybrid-BF by using a combination of HCST and a Modified Breadth First (MBF) traversal. All three algorithms are polynomial in the number of grid squares. Optimized implementations of Hybrid-BF and Hybrid-MBF required less than two seconds on a SUN SPARCstation 10.

Efficient decomposition of polygons into L-shapes with application to VLSI layouts

We present two practical algorithms for partitioning circuit components represented by rectilinear polygons so that they can be stored using the L-shaped corner stitching data structure; that is, our algorithms decompose a simple polygon into a set of nonoverlapping L-shapes and rectangles by using horizontal cuts only. The more general of our algorithms computes and optimal configuration for a wide variety of optimization functions, whereas the other computes a minimum configuration of rectangles and L-shapes. Both algorithms run in <italic>O</italic>(<italic>n</italic> + <italic>h</italic> log <italic>h</italic> time, where <italic>n</italic> is the number of vertices in the polygon and <italic>h</italic> is the number of H-pairs. Because for VLSI data <italic>h</italic> is small, in practice these algorithms are linear in <italic>n</italic>. Experimental results on actual VLSI data compare our algorithms and demonstrate the gains in performance for corner stitching (as measured by different objective functions) obtained by using them instead of more traditional rectangular partitioning algorithms.

Constrained polygon transformations for incremental floorplanning

A productivity-driven methodology for incremental floorplanning is described and the constrained polygon transformation problem, a key step of this methodology, is formulated. The input to the problem consists of a floorplan computed using area estimates and the actual area required for each subcircuit of the floorplan. Informally, the objective is to change the areas of the modules without drastically changing their shapes or locations. We show that the constrained polygon transformation problem is NP-hard and present several fast algorithms that produce results within a few percent of a theoretical lower bound on several floorplans.

Decision tree approximations of Boolean functions

Decision trees are popular representations of Boolean functions. We show that, given an alternative representation of a Boolean function f, say as a read-once branching program, one can find a decision tree T which approximates f to any desired amount of accuracy. Moreover, the size of the decision tree is at most that of the smallest decision tree which can represent f and this construction can be obtained in quasi-polynomial time. We also extend this result to the case where one has access only to a source of random evaluations of the Boolean function f instead of a complete representation. In this case, we show that a similar approximation can be obtained with any specified amount of confidence (as opposed to the absolute certainty of the former case.) This latter result implies proper PAC-learnability of decision trees under the uniform distribution without using membership queries.