DIMACS: Series in Discrete Mathematics and Theoretical Computer Science – serie

This book contains papers presented at the Workshop on Parallel Processing of Discrete Optimization Problems held at DIMACS in April 1994. The contents cover a wide spectrum of the most recent algorithms and applications in parallel processing of discrete optimization and related problems. Topics include parallel branch and bound algorithms, scalability, load balancing, parallelism and irregular data structures and scheduling task graphs on parallel machines. Applications include parallel algorithms for solving satisfiability problems, location problems, linear programming, quadratic and linear assignment problems. This book would be suitable as a textbook in advanced courses on parallel algorithms and combinatorial optimization.

This book contains the proceedings of two workshops on computational aspects of geometric group theory. The workshops, held in the winter of 1994 at DIMACS and at the Geometry Center, covered practical group theoretic computation and theoretical problems. Containing both research and expository articles, this book is the only one available concentrating on the computational aspects of geometric group theory. Because this area involves an interplay between group theory, geometry, and automata theory, the expository articles in this book should help researchers in these fields to make connections to the other areas.

The satisfiability (SAT) problem is central in mathematical logic, computing theory, and many industrial applications. There has been a strong relationship between the theory, the algorithms, and the applications of the SAT problem. This book aims to bring together work by the best theorists, algorithmists, and practitioners working on the SAT problem and on industrial applications, as well as to enhance the interaction between the three research groups. The book features the application of theoretical/algorithmic results to practical problems and presents practical problems for theoretical/algorithmic study.Major topics covered in the book include practical and industrial SAT problems and benchmarks, significant case studies and applications of the SAT problem and SAT algorithms, new algorithms and improved techniques for satisfiability testing, specific data structures and implementation details of the SAT algorithms, and the theoretical study of the SAT problem and SAT algorithms. It features: a comprehensive review of SAT research work over the past 25 years; the most recent research results; and a spectrum of algorithmic issues and applications.

The workshop 'Groups and Computations' took place at the Center for Discrete Mathematics and Theoretical Computer Science (DIMACS) at Rutgers University in June 1995. This and an earlier workshop (see Groups and Computation, Finkelstein and Kantor, c1993, American Mathematical Society) held in October 1991 was aimed at merging theory and practice within the broad area of computation with groups. The primary goal of the previous workshop was to foster a dialogue between researchers studying the computational complexity of group algorithms and those engaged in the development of practical software. It was expected that this would lead to a deeper understanding of the mathematical issues underlying group computation and that this understanding would lead, in turn, to faster algorithms.Comment and subsequent work indicated that this goal had been achieved beyond expectations. The second workshop was designed to reinforce the progress in these directions. The scientific program consisted of invited lectures and research announcements, as well as informal discussions and software demonstrations. The eight extended talks discussed randomization, permutation groups, matrix groups, software systems, fast Fourier transforms and their applications to signal processing and data analysis, computations with finitely presented groups, and implementation and complexity questions. As in the previous workshop, speakers ranged from established researchers to graduate students.

This volume contains research and expository papers by African-American mathematicians on issues related to their involvement in the mathematical sciences. Little is known, taught, or written about African-American mathematicians. Information is lacking on their past and present contributions and on the qualitative and quantitative nature of their existence in and distribution throughout mathematics. This lack of information leads to a number of questions that have to date remained unanswered. This volume provides details and pointers to help answer some of these questions. This title features: research articles by distinguished African-American mathematicians; accomplishments of African-American researchers in the mathematical sciences; and, articles that explore issues important to the African-American community and to the mathematics community as a whole. This book is an inspiration for African-American students who wish to pursue advancement in the mathematical sciences.

This volume features highlights from the DIMACS Special Year on 'Mathematical Support for Molecular Biology'. Top researchers presented both new research results and comprehensive overviews on the use of mathematics (especially discrete mathematics) and theoretical computer science in molecular biology. The book provides a unique 'snapshot' of this growing area of study. It will be of interest to both experts and novices seeking information on the state of the research.

This book contains eleven articles surveying emerging topics in discrete probability. The papers are based on talks given by experts at the DIMACS 'Microsurveys in Discrete Probability' workshop held at the Institute for Advanced Study, Princeton, NJ. This compilation of current research in discrete probability provides a unique overview that is not available elsewhere in book or survey form. Topics covered in the volume include: Markov chains (perfect sampling, coupling from the past, mixing times), random trees (spanning trees on infinite graphs, enumeration of trees and forests, tree-valued Markov chains), distributional estimates (method of bounded differences, Stein-Chen method for normal approximation), dynamical percolation, and Poisson processes. It features surveys written and refereed by experts, and emerging areas of research in discrete probability theory not previously surveyed articles accessible to a broad readership.

Connectivity and facilities location are two important topics in network design, with applications in data communication, transportation, production planning, and VLSI designs. There are two issues concerning these topics: design and optimization. They involve combinatorial design and combinatorial optimization. This volume features talks presented at an interdisciplinary research workshop held at DIMACS in April 1997. The workshop was attended by leading theorists, algorithmists, and practitioners working on network design problems. Finding the solution of design problems and the optimal or approximate solution of the related optimization problem are challenging tasks because no polynomial time algorithms are known.Such problems include some variations of Steiner tree problems (such as multiple-connected Steiner network, independent flow problem, and subset-interconnection designs), topology network design, nonlinear assignment problems (such as quadratic assignment problems), problems in facilities location and allocation, and network problems appearing in VLSI design. The focus of this book is on combinatorial, algorithmic, and applicational aspects of these problems. The volume would be suitable as a textbook for advanced courses in computer science, mathematics, engineering, and operations research.

This volume is based on proceedings held during the DIMACS workshop on Randomization Methods in Algorithm Design in December 1997 at Princeton. The workshop was part of the DIMACS Special Year on Discrete Probability. It served as an interdisciplinary research workshop that brought together a mix of leading theorists, algorithmists and practitioners working in the theory and implementation aspects of algorithms involving randomization. Randomization has played an important role in the design of both sequential and parallel algorithms. The last decade has witnessed tremendous growth in the area of randomized algorithms. During this period, randomized algorithms went from being a tool in computational number theory to finding widespread applications in many problem domains.Major topics covered include randomization techniques for linear and integer programming problems, randomization in the design of approximate algorithms for combinatorial problems, randomization in parallel and distributed algorithms, practical implementation of randomized algorithms, de-randomization issues, and pseudo-random generators. This volume focuses on theory and implementation aspects of algorithms involving randomization. It would be suitable as a graduate or advanced graduate text.

Discrete mathematics stands among the leading disciplines of mathematics and theoretical computer science. This is due primarily to its increasing role in university curricula and its growing importance in applications ranging from optimization to molecular biology. An inaugural conference was held cooperatively by DIMATIA and DIMACS to focus on the versatility, width, and depth of current progress in the subject area. This volume offers a well-balanced blend of research and survey papers reflecting the exciting, attractive topics in contemporary discrete mathematics. Discussed in the book are topics such as graph theory, partially ordered sets, geometrical Ramsey theory, computational complexity issues and applications.

This volume presents the proceedings of a conference held at Princeton University in April 1995 as part of the DIMACS Special Year on Mathematical Support for Molecular Biology. The subject of the conference was the new area of DNA based computing. DNA based computing is the study of using DNA strands as individual computers. The concept was initiated by Leonard Adleman's paper in Science in November 1994.

This volume presents the proceedings from the DIMACS Workshop in Distributed Computing held at Rutgers University. It provides a broad survey of major topics concerning modern applications of networks in the context of distributed computing. Articles included touch upon fundamental problems and challenges related to recent technological advances in the networking industry which are directly relevant and interesting to research on the mathematical principles of distributed computing.Included are issues on diverse areas of networking such as ATM networking technology, issues on routing and flow control in communications networks, security, optical networking and mobile computing. This volume provides state-of-the-art research in these significant areas. The material should acquaint the theoretical community of distributed computing with related issues and problems. Treatment is applied and tailored to industrial advances in networking, however the underlying material presents a rich variety of theoretical problems in distributed computing that carry significant interest and challenge for the modern mathematician.

Time division multiplexing (TDM) has been the fundamental basis for adding capacity to digital telecommunications networks for decades. However, within the past two years, wavelength division multiplexing (WDM) has been emerging as an important and widely deployed complement to TDM. Sales of systems based on the new technology have risen at breathtaking speed. The driving force behind this sales explosion was the unexpected rapid exhaustion of long distance fiber network capacity. This fiber exhaust, combined with favorable economics for WDM, led to the use of this technology over other alternatives. The WDM deployment raises fundamental and challenging problems that require novel and innovative solutions.This volume presents papers from an interdisciplinary workshop held at DIMACS on multichannel optical networks. Leading computer science theorists and practitioners discussed admissions control, routing and channel assignment, multicasting and protection, and fault-tolerance. The book features application of theoretical and/or algorithmical results to practical problems and addresses the influence of practical problems to theoretical/algorithmic studies. The volume can serve as a text for an advanced course in computer science, networking, and operations research.

This volume presents papers related to the DIMACS workshop, ""Codes and Association Schemes"". The articles are devoted to the following topics: applications of association schemes and of the polynomial method to properties of codes, structural results for codes, structural results for association schemes, and properties of orthogonal polynomials and their applications in combinatorics. Papers on coding theory are related to classical topics, such as perfect codes, bounds on codes, codes and combinatorial arrays, weight enumerators, and spherical designs. Papers on orthogonal polynomials provide new results on zeros and symptotic properties of standard families of polynomials encountered in coding theory. The theme of association schemes is represented by new classification results and new classes of schemes related to posets. This volume collects up-to-date applications of the theory of association schemes to coding and presents new properties of both polynomial and general association schemes. It offers a solid representation of results in problems in areas of current interest.

This volume presents selected papers from a three-day workshop held during the DIMACS special years on Mathematical Support for Molecular Biology. Participants from the world over attended, giving the workshop an important international component. The study of discrete mathematics and optimization with medical applications is emerging as an important new research area. Significant applications have been found in medical research, for example in radiosurgical treatment planning, virtual endoscopy, and more. This volume presents a substantive cross-section of active research topics ranging from medical imaging to human anatomy modeling, from gamma knife treatment planning to radiation therapy, and from epileptic seizures to DNA screening. This book is an up-to-date resource reflecting current research directions.

This volume contains the proceedings of the workshop held at the DIMACS Center of Rutgers University (Piscataway, NJ) on Unusual Applications of Number Theory. Standard applications of number theory are to computer science and cryptology. In this volume, well-known number theorist, Melvyn B. Nathanson, gathers articles from the workshop on other, less standard applications in number theory, as well as topics in number theory with potential applications in science and engineering. The material is suitable for graduate students and researchers interested in number theory and its applications.

Algorithmic and quantitative aspects in real algebraic geometry are becoming increasingly important areas of research because of their roles in other areas of mathematics and computer science. The papers in this volume collectively span several different areas of current research. The articles are based on talks given at the DIMACS Workshop on 'Algorithmic and Quantitative Aspects of Real Algebraic Geometry'. Topics include deciding basic algebraic properties of real semi-algebraic sets, application of quantitative results in real algebraic geometry towards investigating the computational complexity of various problems, algorithmic and quantitative questions in real enumerative geometry, new approaches towards solving decision problems in semi-algebraic geometry, as well as computing algebraic certificates, and applications of real algebraic geometry to concrete problems arising in robotics and computer graphics.This book is intended for researchers interested in computational methods in algebra.

This book presents reviewed and revised papers from the fifth and sixth DIMACS Implementation Challenge workshops. These workshops, held approximately annually, aim at encouraging high-quality work in experimental analysis of data structures and algorithms. The papers published in this volume are the results of year-long coordinated research projects and contain new findings and insights. Three papers address the performance evaluation of implementations for two fundamental data structures, dictionaries and priority queues, as used in the context of real applications. Another four papers consider the still evolving topic of methodologies for experimental algorithmics. Five papers are concerned with implementations of algorithms for nearest neighbor search in high dimensional spaces, an area with applications in information retrieval and data mining on collections of Web documents, DNA sequences, images and various other data types.

Consensus methods developed in the context of voting, decision making, and other areas of the social and behavioral sciences have a variety of applications in the biological sciences, originally in taxonomy and evolutionary biology, and more recently in molecular biology. Typically, several alternatives (such as alternative phylogenetic trees, molecular sequences, or alignments) are produced using different methods or under different models, and then one needs to find a consensus solutions.This volume is based on two DIMACS working group meetings on 'bioconsensus'. It provides a valuable introduction and reference to the various aspects of this rapidly developing field. The meetings brought together mathematical and biological scientists to discuss the uses in the biological sciences of methods of consensus and social choice. These two lively meetings contributed much toward establishing the new field of 'bioconsensus'. Yet this book is much more than just a report of two meetings. It includes some historical background, as well as a substantial introduction to the axiomatic foundations of the field of bioconsensus and some practical applications of consensus methods to real data. Also included are contributed papers from experts who were not at the meetings. The book is intended for mathematical biologists, evolutionary biologists, and computer scientists.

This volume is a collection of papers from the DIMACS Workshop on Signal Processing for Wireless Transmission. The workshop brought together theoreticians and practitioners working on wireless communications, information, and coding theory from a variety of perspectives. The main topics discussed in the book are capacity of multiantenna channels, vector broadcast channels and 'dirty-paper' coding, signal processing, and ad hoc networking in wide band channels. These are all major themes in current research in physical-layer design for wireless communication. The book is suitable for graduate students and researchers interested in mathematical problems of communication theory.

This book is a collection of articles written by leading researchers in information theory stemming from the DIMACS Workshop on Network Information held at Rutgers University (Piscataway, NJ). The articles focus on problems concerning efficient and reliable communication in multi-terminal settings. Information theory has recently attracted renewed attention because of key developments spawning challenging research problems. The material is divided into four parts: 'Information Theory for Sources', which concentrates on network source coding problems; 'Information Theory for Channels', where channels, rather than sources, are central to the problem; 'Information Theory for Sources and Channels', which addresses both source and channel coding; and 'Coding', which deals with more practical issues.Mathematicians using applications such as wireless cellular and LAN data services, ad hoc networks and sensor networks will benefit from the developments outlined in these sections. The book is suitable for graduate students and research mathematicians interested in communications and network information theory.

Collected here are papers that were presented at or inspired by the DIMACS workshop, Algebraic Coding Theory and Information Theory (Rutgers University, Piscataway, NJ). Among the topics discussed are universal data compression, graph theoretical ideas in the construction of codes and lattices, decoding algorithms, and computation of capacity in various communications schemes. The book is suitable for graduate students and researchers interested in coding and information theory.

Random projection is a simple geometric technique for reducing the dimensionality of a set of points in Euclidean space while preserving pairwise distances approximately. The technique plays a key role in several breakthrough developments in the field of algorithms. In other cases, it provides elegant alternative proofs. The book begins with an elementary description of the technique and its basic properties. Then it develops the method in the context of applications, which are divided into three groups. The first group consists of combinatorial optimization problems such as maxcut, graph coloring, minimum multicut, graph bandwidth and VLSI layout.Presented in this context is the theory of Euclidean embeddings of graphs. The next group is machine learning problems, specifically, learning intersections of halfspaces and learning large margin hypotheses. The projection method is further refined for the latter application. The last set consists of problems inspired by information retrieval, namely, nearest neighbor search, geometric clustering and efficient low-rank approximation. Motivated by the first two applications, an extension of random projection to the hypercube is developed here. Throughout the book, random projection is used as a way to understand, simplify and connect progress on these important and seemingly unrelated problems. The book is suitable for graduate students and research mathematicians interested in computational geometry.

Studies of the spread and containment of disease rely at heart on a variety of mathematical and computational techniques. This collection aims to introduce the fundamentals of epidemiology and to showcase contemporary work using discrete mathematical techniques. Introductory chapters explain the fundamental concepts of epidemiology, the basic tools provided by mathematics and computer science, and some of the outstanding open problems in the area. Contributed articles then highlight particular problems in monitoring disease outbreaks, vaccination strategies, and modelling disease survival factors, and successfully apply techniques such as formal concept analysis, support vector machines, random graph models, and systems of differential equations. Co-published with the Center for Discrete Mathematics and Theoretical Computer Science beginning with Volume 8. Volumes 1-7 were co-published with the Association for Computer Machinery (ACM). Table of Contents: J. Abello, G. Cormode, D. Fradkin, D. Madigan, O. Melnik, and I. Muchnik -- Selected data mining concepts; D. Schneider -- Descriptive epidemiology: A brief introduction; W. D. Shannon -- Biostatistical challenges in molecular data analysis; L. Hirschman and L. E. Damianos -- Mining online media for global disease outbreak monitoring; D. Ozonoff, A. Pogel, and T. Hannan -- Generalized contingency tables and concept lattices; J. Abello and A. Pogel -- Graph partitions and concept lattices; K. Desai, M.-C. Boily, B. Masse, and R. M. Anderson -- Using transmission dynamics models to validate vaccine efficacy measures prior to conducting HIV vaccine efficacy trials; A. Vazquez -- Causal tree of disease transmission and the spreading of infectious diseases; S. Eubank, V. S. Anil Kumar, M. V. Marathe, A. Srinivasan, and N. Wang -- Structure of social contact networks and their impact on epidemics; J. Abello and M. Capalbo -- Random graphs (and the spread of infections in a social network); S. G. Hartke -- Attempting to narrow the integrality gap for the firefighter problem on trees; J. Li, I. Muchnik, and D. Schneider -- Influences on breast cancer survival via SVM classification in the SEER database; D. Fradkin, I. Muchnik, P. Hermans, and K. Morgan -- Validation of epidemiological models: Chicken epidemiology in the UK; Index. This is a reprint of the 2006 original. (DIMACS/70.S)

Shortest path problems are among the most fundamental combinatorial optimization problems with many applications, both direct and as subroutines. They arise naturally in a remarkable number of real-world settings. A limited list includes transportation planning, network optimization, packet routing, image segmentation, speech recognition, document formatting, robotics, compilers, traffic information systems, and dataflow analysis. Shortest path algorithms have been studied since the 1950's and still remain an active area of research. This volume reports on the research carried out by participants during the Ninth DIMACS Implementation Challenge, which led to several improvements of the state of the art in shortest path algorithms. The infrastructure developed during the Challenge facilitated further research in the area, leading to substantial follow-up work as well as to better and more uniform experimental standards. The results of the Challenge included new cutting-edge techniques for emerging applications such as GPS navigation systems, providing experimental evidence of the most effective algorithms in several real-world settings.

Reliability problems arise with increasing frequency as our systems of telecommunications, information transmission, transportation, and distribution become more and more complex. In December 1989 at DIMACS at Rutgers University, a Workshop on Reliability of Computer and Communication Networks was held to examine the discrete mathematical methods relevant to these problems. There were nearly ninety participants, including theoretical mathematicians, computer scientists, and electrical engineers from academia and industry, as well as network practitioners, engineers, and reliability planners from leading companies involved in the use of computer and communications networks. This volume, published jointly with the Association for Computing Machinery, contains the proceedings from this Workshop. The aim of the Workshop was to identify the latest trends and important open problems, as well as to survey potential practical applications.The Workshop explored questions of computation of reliability of existing systems and of creating new designs to insure high reliability, in addition to the closely related notion of survivability. Redundancy, single stage and multistage networks, interconnected networks, and fault tolerance were also covered. The Workshop emphasized practical applications, with many invited speakers from a variety of companies which are dealing with practical network reliability problems. The success of the Workshop in fostering many new interactions among researchers and practitioners is reflected in the proceedings, which provide an exciting look at some of the major advances at the forefront of this important field of research.

This collection of recent papers on computational complexity theory grew out of activities during a special year at DIMACS. With contributions by some of the leading experts in the field, this book is of lasting value in this fast-moving field, providing expositions not found elsewhere. Although aimed primarily at researchers in complexity theory and graduate students in mathematics or computer science, the book is accessible to anyone with an undergraduate education in mathematics or computer science. By touching on some of the major topics in complexity theory, this book sheds light on this burgeoning area of research.

This volume contains the proceedings of the DIMACS Workshop on Expander Graphs, held at Princeton University in May 1992. The subject of expanding graphs involves a number of different fields and gives rise to important connections among them. Many of these fields were represented at the workshop, including theoretical computer science, combinatorics, probability theory, representation theory, number theory, and differential geometry. With twenty-two talks and two open problem sessions, the workshop provided a unique opportunity for cross-fertilization of various areas. This volume will prove useful to mathematicians and computer scientists interested in current results in this area of research.