Combinatorial Optimization

Clearly written graduate-level text considers the Soviet ellipsoid algorithm for linear programming; efficient algorithms for network flow, matching, spanning trees, and matroids; the theory of NP-complete problems; approximation algorithms ...

Author: Christos H. Papadimitriou

Publisher: Courier Corporation

ISBN: 9780486402581

Category: Mathematics

Page: 496

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Clearly written graduate-level text considers the Soviet ellipsoid algorithm for linear programming; efficient algorithms for network flow, matching, spanning trees, and matroids; the theory of NP-complete problems; approximation algorithms, local search heuristics for NP-complete problems, more. "Mathematicians wishing a self-contained introduction need look no further." — American Mathematical Monthly. 1982 edition.

Algorithms and Complexity

This book constitutes the refereed conference proceedings of the 11th International Conference on Algorithms and Complexity, CIAC 2019, held in Rome, Italy, in May 2019.

Author: Pinar Heggernes

Publisher: Springer

ISBN: 3030174018

Category: Computers

Page: 378

View: 796

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This book constitutes the refereed conference proceedings of the 11th International Conference on Algorithms and Complexity, CIAC 2019, held in Rome, Italy, in May 2019. The 30 full papers were carefully reviewed and selected from 95 submissions. The International Conference on Algorithms and Complexity is intended to provide a forum for researchers working in all aspects of computational complexity and the use, design, analysis and experimentation of efficient algorithms and data structures. The papers present original research in the theory and applications of algorithms and computational complexity.

Counting Sampling and Integrating Algorithms and Complexity

A major theme of the book is the idea of accumulating information about a set of combinatorial structures by performing a random walk on those structures.

Author: Mark Jerrum

Publisher: Springer Science & Business Media

ISBN: 3764369469

Category: Mathematics

Page: 112

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The subject of these notes is counting and related topics, viewed from a computational perspective. A major theme of the book is the idea of accumulating information about a set of combinatorial structures by performing a random walk on those structures. These notes will be of value not only to teachers of postgraduate courses on these topics, but also to established researchers. For the first time this body of knowledge has been brought together in a single volume.

Algorithms and Complexity

This book constitutes the refereed conference proceedings of the 12th International Conference on Algorithms and Complexity, CIAC 2019, held as a virtual event, in May 2021.

Author: Tiziana Calamoneri

Publisher: Springer Nature

ISBN: 9783030752422

Category:

Page:

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Algorithms and Complexity

The monotonicity of an algorithm gained relevance in the context of mechanism design. If each machine speed is only known to the machine itself, ...

Author: Tiziana Calamoneri

Publisher: Springer Science & Business Media

ISBN: 9783540343752

Category: Computers

Page: 394

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This book constitutes the refereed proceedings of the 6th Italian Conference on Algorithms and Computation, CIAC 2006, held in Rome, Italy, in May 2006. The 33 revised full papers presented together with 3 invited papers were carefully reviewed and selected from 80 submissions. Among the topics addressed are sequential, parallel and distributed algorithms, data structures, approximation algorithms, randomized algorithms, on-line algorithms, graph algorithms, analysis of algorithms, algorithm engineering, algorithmic game theory, computational biology, computational complexity, communication networks, computational geometry, cryptography, discrete optimization, graph drawing, mathematical programming, and quantum algorithms.

Algorithms and Complexity

... "K-complexity", "Kolmogorov-Chaitin randomness", "algorithmic complexity", ... primarily in connection with the analysis and synthesis of algorithms in ...

Author: Bozzano G Luisa

Publisher: Elsevier

ISBN: 0444880712

Category: Computers

Page: 996

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The second part of this Handbook presents a choice of material on the theory of automata and rewriting systems, the foundations of modern programming languages, logics for program specification and verification, and some chapters on the theoretic modelling of advanced information processing.

A Guide to Algorithm Design

Drawing on the authors’ classroom-tested material, this text takes readers step by step through the concepts and methods for analyzing algorithmic complexity.

Author: Anne Benoit

Publisher: CRC Press

ISBN: 9781439898130

Category: Computers

Page: 380

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Presenting a complementary perspective to standard books on algorithms, A Guide to Algorithm Design: Paradigms, Methods, and Complexity Analysis provides a roadmap for readers to determine the difficulty of an algorithmic problem by finding an optimal solution or proving complexity results. It gives a practical treatment of algorithmic complexity and guides readers in solving algorithmic problems. Divided into three parts, the book offers a comprehensive set of problems with solutions as well as in-depth case studies that demonstrate how to assess the complexity of a new problem. Part I helps readers understand the main design principles and design efficient algorithms. Part II covers polynomial reductions from NP-complete problems and approaches that go beyond NP-completeness. Part III supplies readers with tools and techniques to evaluate problem complexity, including how to determine which instances are polynomial and which are NP-hard. Drawing on the authors’ classroom-tested material, this text takes readers step by step through the concepts and methods for analyzing algorithmic complexity. Through many problems and detailed examples, readers can investigate polynomial-time algorithms and NP-completeness and beyond.

Algorithms and Complexity

Springer, Heidelberg (2001) Kratochv ́ıl, J., Tsuza, Z.: Algorithmic complexity of list colorings. Discrete Applied Mathematics 50, 297–302 (1994) Kratsch, ...

Author: Paul G. Spirakis

Publisher: Springer

ISBN: 9783642382338

Category: Computers

Page: 384

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This book constitutes the refereed conference proceedings of the 8th International Conference on Algorithms and Complexity, CIAC 2013, held in Barcelona, Spain, during May 22-24, 2013. The 31 revised full papers presented were carefully reviewed and selected from 75 submissions. The papers present current research in all aspects of computational complexity and the use, design, analysis and experimentation of efficient algorithms and data structures.

Algorithms and Complexity

9, 558–565 (1980) Manlove, D.F.: On the algorithmic complexity of twelve covering and independence parameters of graphs. Disc. Appl. Math.

Author: Pinar Heggernes

Publisher: Springer

ISBN: 9783030174026

Category: Computers

Page: 378

View: 595

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This book constitutes the refereed conference proceedings of the 11th International Conference on Algorithms and Complexity, CIAC 2019, held in Rome, Italy, in May 2019. The 30 full papers were carefully reviewed and selected from 95 submissions. The International Conference on Algorithms and Complexity is intended to provide a forum for researchers working in all aspects of computational complexity and the use, design, analysis and experimentation of efficient algorithms and data structures. The papers present original research in the theory and applications of algorithms and computational complexity.

The Steiner Tree Problem

No specific previous knowledge is assumed. The central theme of the book is a geometrical problem dating back to Jakob Steiner.

Author: Hans Jürgen Prömel

Publisher: Springer Science & Business Media

ISBN: 9783322802910

Category: Mathematics

Page: 241

View: 283

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In recent years, algorithmic graph theory has become increasingly important as a link between discrete mathematics and theoretical computer science. This textbook introduces students of mathematics and computer science to the interrelated fields of graphs theory, algorithms and complexity.

Computational Complexity

New and classical results in computational complexity, including interactive proofs, PCP, derandomization, and quantum computation. Ideal for graduate students.

Author: Sanjeev Arora

Publisher: Cambridge University Press

ISBN: 9780521424264

Category: Computers

Page: 579

View: 936

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New and classical results in computational complexity, including interactive proofs, PCP, derandomization, and quantum computation. Ideal for graduate students.

Matrix Partitions of Graphs

Recently, there has been much interest in studying certain graph partitions that generalize graph colourings and homomorphisms.

Author: Mayssam Mohammadi Nevisi

Publisher:

ISBN: OCLC:1125370337

Category:

Page: 108

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Recently, there has been much interest in studying certain graph partitions that generalize graph colourings and homomorphisms. They are described by a pattern, usually viewed asa symmetric $\{0, 1, *\}$-matrix $M$. Existing results focus on recognition algorithms and characterization theorems for graphsthat admit such $M$-partitions, or $M$-partitions in which vertices of the input graph $G$have lists of admissible parts. For (homomorphism) problems with costs, researchers havealso investigated the approximability of the problem.In this thesis, we study the complexity of these matrix partition problems.First, we investigate the complexity of counting $M$-partitions. The complexity of counting problemsfor graph colourings and graph homomorphisms has been previously classified, and most turned out to be $\sharpP$-complete, with only trivial exceptions.By contrast, we exhibit many $M$-partition problems with interesting non-trivial counting algorithms; moreover these algorithms appear to depend on highly combinatorial tools. In fact, our tools are sufficient to classify the complexity of counting$M$-partitions for all matrices $M$ of size less than four.Then, we turn our attention to the homomorphism problems with costs.Previous results include partial classification of approximation complexityfor doubly convex bipartite graphs.We complete these results and extend them to all digraphs.We prove that if $H$ is a co-circular arc bigraph,then the minimum cost graph homomorphism problem to $H$ admits a polynomial time constant ratio approximation algorithm.This solves a problem posed in an earlier paper. Our algorithm is obtained by derandomizinga two-phase randomized procedure. In the final third of the thesis, we present a partial dichotomy forthe complexity of exact minimization of homomorphism costs,when the cost function is a constant across the vertices of the input graph. We show that the dichotomy is complete when the target graph is a tree.

Computational Complexity

This new text offers a comprehensive and accessible treatment of the theory of algorithms and complexity - the elegant body of concepts and methods developed by computer scientists over the past 30 years for studying the performance and ...

Author: Christos H. Papadimitriou

Publisher: Pearson

ISBN: STANFORD:36105003441289

Category: Computers

Page: 523

View: 674

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The first unified introduction and reference for the field of computational complexity. Virtually non-existent only 25 years ago, computational complexity has expanded tremendously and now comprises a major part of the researh activity in theoretical science.

Using Additional Information in Streaming Algorithms

Streaming problems are algorithmic problems that are mainly characterized by their massive input streams.

Author: Raffael Buff

Publisher: diplom.de

ISBN: 9783961160426

Category: Computers

Page: 125

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Streaming problems are algorithmic problems that are mainly characterized by their massive input streams. Because of these data streams, the algorithms for these problems are forced to be space-efficient, as the input stream length generally exceeds the available storage. In this thesis, the two streaming problems most frequent item and number of distinct items are studied in detail relating to their algorithmic complexities, and it is compared whether the verification of solution hypotheses has lower algorithmic complexity than computing a solution from the data stream. For this analysis, we introduce some concepts to prove space complexity lower bounds for an approximative setting and for hypothesis verification. For the most frequent item problem which consists in identifying the item which has the highest occurrence within the data stream, we can prove a linear space complexity lower bound for the deterministic and probabilistic setting. This implies that, in practice, this streaming problem cannot be solved in a satisfactory way since every algorithm has to exceed any reasonable storage limit. For some settings, the upper and lower bounds are almost tight, which implies that we have designed an almost optimal algorithm. Even for small approximation ratios, we can prove a linear lower bound, but not for larger ones. Nevertheless, we are not able to design an algorithm that solves the most frequent item problem space-efficiently for large approximation ratios. Furthermore, if we want to verify whether a hypothesis of the highest frequency count is true or not, we get exactly the same space complexity lower bounds, which leads to the conclusion that we are likely not able to profit from a stated hypothesis. The number of distinct items problem counts all different elements of the input stream. If we want to solve this problem exactly (in a deterministic or probabilistic setting) or approximately with a deterministic algorithm, we require once again linear storage size which is tight to the upper bound. However, for the approximative and probabilistic setting, we can enhance an already known space-efficient algorithm such that it is usable for arbitrarily small approximation ratios and arbitrarily good success probabilities. The hypothesis verification leads once again to the same lower bounds. However, there are some streaming problems that are able to profit from additional information such as hypotheses, as e.g., the median problem.

Algorithmic Complexity and Telecommunication Problems

This is followed by three chapters which explore the key area of information communication.

Author: J-P Barthelmy

Publisher: CRC Press

ISBN: 9781000159431

Category: Computers

Page: 276

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In this treatment of algorithmic complexity the authors explore an area fundamental to the study of the foundations of computer science. It is a topic which is at the interface of information theory, applied mathematics and computer language theory and which is rooted strongly in this book in the problems of computer communication.; Complexity theory classifies problems according to the difficulty of resolving them, while algorithms provide the computational method for solving those problems. Therefore, algorithmic complexity is concerned with establishing the best algorithm given the constraints of the computational environment and the degree of complexity.; The first three chapters present the context for a later in-depth look at applied areas of the subject, with an outline of classical complexity theory. This is followed by three chapters which explore the key area of information communication. Within this field, the book is particularly concerned with two contiguous areas which make contrasting demands on the application of algorithmic complexity. Cryptography demands the creation of extremely complex problems in order to achieve its goal of security, whereas in coding for communication the emphasis is on maximizing the compact nature of the message and providing the error correction necessary for the message to achieve optimum speed. The two must co-exist and the methods outlined in "Algorithmic Complexity" suggest a number of approaches to such problems based on extensive examples of the authors' experience.; This senior undergraduate book should be an essential read for those studying advanced topics in theoretical computer science and should provide an introduction to applied complexity for researchers and professionals alike.

Algorithms and Complexity

The Algorithmic Complexity of Chemical Threshold Testing Peter Damaschke FernUniversität , Theoretische Informatik II 58084 Hagen , Germany Peter.

Author:

Publisher:

ISBN: UOM:39015040320312

Category: Algorithms

Page:

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Combinatorial Optimization

Often , when implementing a graph algorithm , a subset of this structure ... Background literature on algorithms and complexity Background literature on ...

Author: Alexander Schrijver

Publisher: Springer Science & Business Media

ISBN: 3540443894

Category: Business & Economics

Page: 1881

View: 509

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From the reviews: "About 30 years ago, when I was a student, the first book on combinatorial optimization came out referred to as "the Lawler" simply. I think that now, with this volume Springer has landed a coup: "The Schrijver". The box is offered for less than 90.- EURO, which to my opinion is one of the best deals after the introduction of this currency." OR-Spectrum

State Space Search

This book is particularly concerned with heuristic state-space search for combinatorial optimization.

Author: Weixiong Zhang

Publisher: Springer Science & Business Media

ISBN: 9781461215387

Category: Computers

Page: 201

View: 855

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This book is particularly concerned with heuristic state-space search for combinatorial optimization. Its two central themes are the average-case complexity of state-space search algorithms and the applications of the results notably to branch-and-bound techniques. Primarily written for researchers in computer science, the author presupposes a basic familiarity with complexity theory, and it is assumed that the reader is familiar with the basic concepts of random variables and recursive functions. Two successful applications are presented in depth: one is a set of state-space transformation methods which can be used to find approximate solutions quickly, and the second is forward estimation for constructing more informative evaluation functions.

Network Optimization Problems Algorithms Applications and Complexity

In the past few decades, there has been a large amount of work on algorithms for linear network flow problems, special classes of network problems such as assignment problems (linear and quadratic), Steiner tree problem, topology network ...

Author: D Z Du

Publisher: World Scientific

ISBN: 9789814504584

Category:

Page: 416

View: 825

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In the past few decades, there has been a large amount of work on algorithms for linear network flow problems, special classes of network problems such as assignment problems (linear and quadratic), Steiner tree problem, topology network design and nonconvex cost network flow problems. Network optimization problems find numerous applications in transportation, in communication network design, in production and inventory planning, in facilities location and allocation, and in VLSI design. The purpose of this book is to cover a spectrum of recent developments in network optimization problems, from linear networks to general nonconvex network flow problems. Contents:Greedily Solvable Transportation Networks and Edge-Guided Vertex Elimination (I Adler & R Shamir)Networks Minimizing Length Plus the Number of Steiner Points (T Colthurst et al.)Practical Experiences Using an Interactive Optimization Procedure for Vehicle Scheduling (J R Daduna et al.)Subset Interconnection Designs: Generalizations of Spanning Trees and Steiner Trees (D-Z Du & P M Pardalos)Polynomial and Strongly Polynomial Algorithms for Convex Network Optimization (D S Hochbaum)Hamiltonian Circuits for 2-Regular Interconnection Networks (F K Hwang & W-C W Li)Equivalent Formulations for the Steiner Problem in Graphs (B N Khoury et al.)Minimum Concave-Cost Network Flow Problems with a Single Nonlinear Arc Cost (B Klinz & H Tuy)A Method for Solving Network Flow Problems with General Nonlinear Arc Costs (B W Lamar)Application of Global Line Search in Optimization of Networks (J Mockus)Solving Nonlinear Programs with Embedded Network Structures (M Ç Pinar & S A Zenios)On Algorithms for Nonlinear Dynamic Networks (W B Powell et al.)Strategic and Tactical Models and Algorithms for the Coal Industry Under the 1990 Clean Air Act (H D Sherali & Q J Saifee)Multi-Objective Routing in Stochastic Evacuation Networks (J M Smith)A Simplex Method for Network Programs with Convex Separable Piecewise Linear Costs and Its Application to Stochastic Transshipment Problems (J Sun et al.)A Bibliography on Network Flow Problems (M Veldhorst)Tabu Search: Applications and Prospects (S Voß)The Shortest Path Network and Its Applications in Bicriteria Shortest Path Problems (G-L Xue & S-Z Sun)A Network Formalism for Pure Exchange Economic Equilibria (L Zhao & A Nagurney)Steiner Problem in Multistage Computer Networks (S Bhattacharya & B Dasgupta) Readership: Applied mathematicians. keywords:“This volume reflects the wide spectrum of recent research activities in the design and analysis of algorithms and the applications of networks.”Journal of Global Optimization